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All Textbook Solutions for Introductory Statistics

Table 8.2 shows a different random sampling of 20 cell phone models. Use this data to calculate a 93% confidence interval for the true mean SAR for cell phones certified for use In the United States. As prevIous1y assume that the population standard deviation is a = 0.337. Table 8.2 Phone Model SAR Phone Model SAR Blackberry Pearl 8120 1.48 Nokia E71x 1.53 HTC Evo Design 4G 0.8 Nokia N75 0.68 HTC Freestyle 1.15 Nokia N79 1.4 LG My 1.36 Sagem Puma 1.24 LG Fathom 0.77 Samsung Fascinate 0.57 LG Opumus Vu 0.462 Samsung Infuse 4G 0.2 Motorola Cliq XT 1.36 Samsung Nexus S 0.51 Motorola Droid Pro 1.39 Samsung Replenish 0.3 Motorola Dro,d Razr M 1.3 Sony W518a Waikman 0.73 Nokia 7705 Twist 0.7 ZTE C79 0.869 Refer back to the pizza-delivery Try It exercise. The population standard deviation Is six minutes and the sample mean deliver time Is 36 minutes. Use a sample size of 20. Find a 95% confidence interval estimate for the true mean pizza delivery time.Refer back to the pizza-deliver Try It exercise. The mean delivery time is 36 minutes and the population standard deviation is six minutes. Assume the sample size is changed to 50 restaurants with the same sample mean. Find a 90% confidence Interval estimate for the population mean delivery time.Suppose we know that a confidence interval is (42.12,47.88). Find the error bound and the sample mean.The population standard deviation for the height of high school basketball players is three inches. If we want to be 95% confident that the sample mean height is within one inch of the true population mean height, how many randomly selected students must be surveyed?You do a study of hypnotherapy to determine how effective ft is In Increasing the number of hours of sleep subjects get each night. You measure hours of sleep for 12 subjects with the following results. Construct a 95% confidence Interval for the mean number of bout-s slept for the population (assumed normal) from which you took the data. 8.2; 9.1; 7.7; 8.6; 6.9; 11.2; 10.1; 9.9. 8.9. 9.2; 7.5; 10.5 A random sample of statistics students were asked to estimate the total number of hours they spend watching television in an average week. The responses are recorded In Table 8.4. Use this sample data to construct a 98% confidence Interval for the mean number of hours statistics students will spend watching television In one week. Table 8.4 0 3 1 20 9 5 10 1 10 4 14 2 4 4 5 Suppose 250 randomly selected people are surveyed to determine if they own a tablet. Of the 250 surveyed, 98 reported owning a tablet. Using a 95% confidence level, compute a confidence interval estimate for the true proportion of people who own tablets.A student polls his school to see If students In the school district are for or against the new legislation regarding school uniforms. She surveys 600 students and finds that .180 are against the new legislation. a. Compute a 90% confidence Interval for the true percent of students who are against the new legislation, and interpret the confidence Interval. b. In a sample of 300 students, 68% said they own an iPod and a smart phone. Compute a 97% confidence interval for the true percent of students who own an IPod and a smartphone.Out of a random sample of 65 freshmen at State University, 31 students have declared a major. Use the “plus- four” method to find a 9600 confidence interval for the true proportion of freshmen at State University who have declared a major.The Berkman Center Study referenced in Example 8.13 talked to teens In smaller focus groups, but also Interviewed additional teens over the phone. When the study was complete, 588 teens had answered the question about their Facebook friends wIth 159 savIng that the have more than 500 frIends. Use the “plus-four” method to find a 90% confidence Interval for the true proportion of teens that would report having more than 500 Facebook friends based on this larger sample. Compare the results to those in Example 8.13.Suppose an Internet marketing company wants to determine the cunent percentage of customers who click on ads on their smartphones. How many customers should the company survey in order to be 90% confident that the estimated proportion Is within five percentage points of the ue population proportion of customers who click on ads on their smartphones?Use the following information to answer the next five exercises: The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 2.1-1 pounds. The sample standard deviation is 11 pounds. Identify the following: a. x ___ b= ___ C. n= ____Use the following information to answer the next five exercises: The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 2.1-1 pounds. The sample standard deviation is 11 pounds. 2. In words, define the random variables X and X.Use the following information to answer the next five exercises: The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 2.1-1 pounds. The sample standard deviation is 11 pounds Which distribution should you use for this problem?Use the following information to answer the next five exercises: The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 2.1-1 pounds. The sample standard deviation is 11 pounds Construct a 95°o confidence intera1 for the population mean weight of newborn elephants. State the confidence interval, sketch the graph, and calculate the error bound.Use the following information to answer the next five exercises: The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 2.1-1 pounds. The sample standard deviation is 11 pounds What will happen to the confidence Interval obtained, If 500 newborn elephants are weighed Instead of 50? Why?Use (he following information to answer the next sewn exercises: The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There is a known standard deviation of 2.2 minutes. The population distribution is assumed to be normal. 6. Identify the following: a. X = ______ b. = ____ C. n= ____Use (he following information to answer the next sewn exercises: The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There is a known standard deviation of 2.2 minutes. The population distribution is assumed to be normal. 7. In words, define the random variables X and X.Use the following information to answer the next sewn exercises: The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There Is a known standard deviation of 2.2 minutes. The population distribudon Is assumed to be normal. Which distribution should you use for this problem?Use the following information to answer the next sewn exercises: The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There Is a known standard deviation of 2.2 minutes. The population distribudon Is assumed to be normal. Construct a 90% confidence interal for the population mean nine to complete the forms. State the confidence intervals sketch the graph, and cakulate the enor bound.Use the following information to answer the next sewn exercises: The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There Is a known standard deviation of 2.2 minutes. The population distribudon Is assumed to be normal. 10. If the Census wants to increase ks level of confidence and keep the error bound the same by taking another survey, what changes should it make?Use the following information to answer the next sewn exercises: The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There Is a known standard deviation of 2.2 minutes. The population distribudon Is assumed to be normal. If the Census did another survey kept the error bound the same. and surveyed only 50 people instead of 200, what would happen to the level of confidence? Why?Use the following information to answer the next en exercises: A sample of 20 beads of lettuce was selected. Assume that the population distribution of bead we1gu Is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. Identify the following: a. X =________ b. = _ C. n= ____Use the following information to answer the next en exercises: A sample of 20 beads of lettuce was selected. Assume that the population distribution of bead we1gu Is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. Identify the following: a. X =________ b. = _ C. n= ____Use the following information to answer the next en exercises: A sample of 20 beads of lettuce was selected. Assume that the population distribution of bead we1gu Is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. In words, define the random variable X.Use the following information to answer the next en exercises: A sample of 20 beads of lettuce was selected. Assume that the population distribution of bead we1gu Is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. In words, define the random variable X Use the following information to answer the next en exercises: A sample of 20 beads of lettuce was selected. Assume that the population distribution of bead we1gu Is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. Which distribution should you use for this problem?Use the following information to answer the next en exercises: A sample of 20 beads of lettuce was selected. Assume that the population distribution of bead we1gu Is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. Construct a 90% confidence interval for the population mean weight of the heads of lettuce. State the confidence interval, sketch the graph, and calculate the error bound.Use the following information to answer the next en exercises: A sample of 20 beads of lettuce was selected. Assume that the population distribution of bead we1gu Is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. Construct a 95°c confidence interval for the population mean weight of the heads of lettuce. State the confidence Interval, sketch the graph, and calculate the error bound.Use the following information to answer the next en exercises: A sample of 20 beads of lettuce was selected. Assume that the population distribution of bead we1gu Is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. In complete sentences, explain why the confidence interval in Exercise 8.17 is larger than in Exercise 8.18.Use the following information to answer the next en exercises: A sample of 20 beads of lettuce was selected. Assume that the population distribution of bead we1gu Is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. In complete sentences, give an interpretation of what the interval in Exercise 8.18 means.Use the following information to answer the next en exercises: A sample of 20 beads of lettuce was selected. Assume that the population distribution of bead we1gu Is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. What would happen if 40 heads of lettuce were sampled instead of 20, and the error bound remained the same?Use the following information to answer the next en exercises: A sample of 20 beads of lettuce was selected. Assume that the population distribution of bead we1gu Is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. What would happen if .10 heads of lettuce were sampled instead of 20, and the confidence level remained the same?Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. 23 Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. n=_____Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student _____________=15 Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student In words, define the random variable X .Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student 27. What is x estimating?Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. 28. Is xknown?Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. As a result of your answer to Exercise 8.26. state the exact distribution to use when calculating the confidence interval.Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. Construct a 95% Confidence Interval for the true mean age of P.4nrer Foothill College swderns by working out then answering the next seven exercises. How much area is in both tails (combined)? a =________Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. Construct a 95% Confidence Interval for the true mean age of P.4nrer Foothill College swderns by working out then answering the next seven exercises. How much area is in each tail=_________Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. Construct a 95% Confidence Interval for the true mean age of P.4nrer Foothill College swderns by working out then answering the next seven exercises. 32. Identify the following specifications: a. lower limit b. upper limit c. error bound Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. Construct a 95% Confidence Interval for the true mean age of P.4nrer Foothill College swderns by working out then answering the next seven exercises. 33. The 95% confidence interval is:__________.Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. Construct a 95% Confidence Interval for the true mean age of P.4nrer Foothill College swderns by working out then answering the next seven exercises. 34. Fill In the blanks on the graph with the areas, upper and lower limits of the confidence interval, and the sample mean. Figure 8.8 Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. Construct a 95% Confidence Interval for the true mean age of P.4nrer Foothill College swderns by working out then answering the next seven exercises. In one complete sentence, explain what the interval means.Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. Construct a 95% Confidence Interval for the true mean age of P.4nrer Foothill College swderns by working out then answering the next seven exercises. Using the same mean, standard deviation, and level of confidence, suppose that n were 69 instead of 25. Would the error bound become larger or smaller? How do you know?Use the following information to answer the next 14 exercises: The mean age for all Foothill College students for a recent Fall term was 33.2. The population standard deviation has been pretty consistent at 15. Suppose that twenty-five Winter students were randomly selected. The mean age for the sample was 30.4. We are interested in the true mean age for Winter Foothill College students. Let X = the age of a Winter Foothill College student. Construct a 95% Confidence Interval for the true mean age of P.4nrer Foothill College swderns by working out then answering the next seven exercises. Using the same mean, standard deviation, and sample size. how would the enor bound change if the confidence level were reduced to 90%? Why?Use the following information to answer (he next five exercises. A hospital is trying to cut down on emergency room waft times. It Is interested in the amount of time patients must wait before being called back to be examined. An Investigation committee randomly surveyed 70 patients. The sample mean was 1.5 bows with a sample standard deviation of 0.5 hours. 38. Identify the following: a. x ____ b. sx=_____. c. n =_____ d. n-1=______ .Use the following information o answer (he ne.t jut exercises. A hospital Is trying to cut down on ernergency room waft times. It Is interested In the amount of time patients must wait before being called back to be examined. An Investigation committee iandom1v sureved 70 patients. The sample mean was 1.5 bows with a sample standard deviation of 0.5 hours. Define the random variables X and in words.Use the following information o answer (he ne.t jut exercises. A hospital Is trying to cut down on ernergency room waft times. It Is interested In the amount of time patients must wait before being called back to be examined. An Investigation committee iandom1v sureved 70 patients. The sample mean was 1.5 bows with a sample standard deviation of 0.5 hours. Which distribution should you use for this problem?Use the following information o answer (he ne.t jut exercises. A hospital Is trying to cut down on ernergency room waft times. It Is interested In the amount of time patients must wait before being called back to be examined. An Investigation committee iandom1v surveyed 70 patients. The sample mean was 1.5 bows with a sample standard deviation of 0.5 hours. Construct a 9500 confidence thtera1 for the population mean time spent waiting. State the cotafidence interval, sketch the graph, and calculate the enor bound.Use the following information o answer the next jut exercises. A hospital Is trying to cut down on emergency room waft times. It Is interested In the amount of time patients must wait before being called back to be examined. An Investigation committee iandom1v surveyed 70 patients. The sample mean was 1.5 bows with a sample standard deviation of 0.5 hours. 42. Explain in complete sentences what the confidence interval means.Use the following information answer the next six exercses: One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that the watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal. Identify the following: a. x ____ b. s= C. n= d. n-1=_____Use the following information answer the next six exercses: One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that the watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal. 44. Define the random variable X in words.Use the following information answer the next six exercses: One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that the watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal. 45. Define the random variable X X in words.Use the following information answer the next six exercses: One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that the watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal. 46. Which distribution should you use for this problem?Use the following information answer the next six exercses: One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that the watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal. Construct a 99% confidence interval for the population mean hours spent watching television per month. (a) State the confidence interval, (b) sketch the graph. and (C) calculate the error bound.Use the following information answer the next six exercses: One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that the watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal. Why would the error bound change if the confidence level were lowered to 95%?Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 49. Calculate the following: a.x =_; _ b. sx=c. n=Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 Define the random variable X X in words.Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 What is Xestimating?Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10Is x known?Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 As a result of your answer to Exercise 8.52. state the exact distribution to use when calculating the confidence interval.Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 Construct a 95% confidence interval for the true mean number of colors on national flags. How much area is in both tails (combined)?Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 Construct a 95% confidence interval for the true mean number of colors on national flags. How much area is in each tail?Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 Construct a 95% confidence interval for the true mean number of colors on national flags. Calculate the following: a. lower limit b. upper limit c. error bound Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 Construct a 95% confidence interval for the true mean number of colors on national flags. The 95% confidence interval is_____Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 Construct a 95% confidence interval for the true mean number of colors on national flags. 58. Fill In the blanks on the graph with the areas, the upper and lower limits of the Confidence Interval and the sample mean. Figure 8.9 Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 Construct a 95% confidence interval for the true mean number of colors on national flags. 59. In one complete sentence, explain what the interval means.Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 Construct a 95% confidence interval for the true mean number of colors on national flags. Using the same x , sx , and level of confidence, suppose that n were 69 instead of 39. Would the error bound become larger or smaller? How do you know?Use the following information to answer the next 13 exercises: The data In Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag. X Freq. 1 1 2 7 3 18 4 7 5 6 Table 8.10 Construct a 95% confidence interval for the true mean number of colors on national flags. Using the same x,sxs, and n =39, how would the error bound change If the confidence level were reduced to 90%? Why?Use (he following information o answer the next two exercises: Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions. When designing a study to determine this population proportion, what Is the minimum number you would need to survey to be 90% confident that the population proportion Is estimated to within 0.05?Use the following information o answer the next two exercises: Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions. If it were later determined that it was important to be more than 90% confident and a new survey were commissioned, how would It affect the minimum number you need to survey? Why?Use the following information o answer the next two exercises: Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions. 64. Identify the following: a. x= _____ b. n= ____ c. p’=Use the following information o answer the next two exercises: Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions. Define the random variables X and P’ in words.Use the following information o answer the next two exercises: Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions. Which distribution should you use for this problem?Use the following information o answer the next two exercises: Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions. Construct a 95°o confidence interval for the population proportion of households where the women make the majority of the purchasing decisions. State the confidence interval, sketch the graph, and calculate the error bound.Use the following information o answer the next two exercises: Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions. List two difficulties the company might have in obtaining random results, If this survey were done by email.Use the following information to answer the next flue exerrises’ Of 1,050 randomly selected adults. 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage earners. 250 identified themselves as mid- level managers, and 160 identified themselves as executives. In the survey, 82% of manual laborers preferred trucks, 620% of non-manual wage earners preferred trucks, 5-1% of mid-level managers preferred trucks, and 26% of executives preferred nicks. We are interested in finding the 95% confidence interval for the percent of executives who prefer trucks. Define random variables X and P in words.Use the following information to answer the next flue exerrises’ Of 1,050 randomly selected adults. 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage earners. 250 identified themselves as mid- level managers, and 160 identified themselves as executives. In the survey, 82% of manual laborers preferred trucks, 620% of non-manual wage earners preferred trucks, 5-1% of mid-level managers preferred trucks, and 26% of executives preferred trucks. Which distribution should you use for this problem?Use the following information to answer the next flue exerrises’ Of 1,050 randomly selected adults. 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage earners. 250 identified themselves as mid- level managers, and 160 identified themselves as executives. In the survey, 82% of manual laborers preferred trucks, 620% of non-manual wage earners preferred trucks, 5-1% of mid-level managers preferred trucks, and 26% of executives preferred trucks. 71.. Construct a 95% confidence interval. State the confidence interval, sketch the graph, and calculate the error bound.Use the following information to answer the next flue exerrises’ Of 1,050 randomly selected adults. 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage earners. 250 identified themselves as mid- level managers, and 160 identified themselves as executives. In the survey, 82% of manual laborers preferred trucks, 620% of non-manual wage earners preferred trucks, 5-1% of mid-level managers preferred trucks, and 26% of executives preferred trucks. Suppose we want to lower the sampling error. What is one way to accomplish that?Use the following information to answer the next flue exerrises’ Of 1,050 randomly selected adults. 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage earners. 250 identified themselves as mid- level managers, and 160 identified themselves as executives. In the survey, 82% of manual laborers preferred trucks, 620% of non-manual wage earners preferred trucks, 5-1% of mid-level managers preferred trucks, and 26% of executives preferred trucks. The sampling error given in the survey is 2%. Explain what the 2% means.Use the following information to answer the next five exercises: A po11 of 1.200 voters asked what the most significant Issue was in the upcoming election. Sixty-five percent answered the economy We are interested in the population proportion of voters who feel the economy Is the most important. 74. Define the random variable X in words.Use the following information to answer the next five exercises: A po11 of 1.200 voters asked what the most significant Issue was in the upcoming election. Sixty-five percent answered the economy We are interested in the population proportion of voters who feel the economy Is the most important. Define the random variable P’ in words.Use the following information to answer the next five exercises: A po11 of 1.200 voters asked what the most significant Issue was in the upcoming election. Sixty-five percent answered the economy We are interested in the population proportion of voters who feel the economy Is the most important. Which distribution should you use for this problem?Use the following information to answer the next five exercises: A po11 of 1.200 voters asked what the most significant Issue was in the upcoming election. Sixty-five percent answered the economy We are interested in the population proportion of voters who feel the economy Is the most important. Construct a 90% confidence interval, and state the confidence interval and the error bound.Use the following information to answer the next five exercises: A po11 of 1.200 voters asked what the most significant Issue was in the upcoming election. Sixty-five percent answered the economy We are interested in the population proportion of voters who feel the economy Is the most important. What would happen to the confidence interval if the level of confidence were 95%?Use the following information to answer the next five exercises: A po11 of 1.200 voters asked what the most significant Issue was in the upcoming election. Sixty-five percent answered the economy We are interested in the population proportion of voters who feel the economy Is the most important. What is being counted?Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the ice Chalet. Assume that the children in the selected class are a random sample of the population. In words, define the random variable X.Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the ice Chalet. Assume that the children in the selected class are a random sample of the population. 81. Calculate the following: a. x= ______ b. n= _____ C. p’=___Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the ice Chalet. Assume that the children in the selected class are a random sample of the population. State the estimated distribution of X. X~________Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the ice Chalet. Assume that the children in the selected class are a random sample of the population. Define a new random variable P. What is p’ estimating?Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the ice Chalet. Assume that the children in the selected class are a random sample of the population. 84. In words, define the random variable P.Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the ice Chalet. Assume that the children in the selected class are a random sample of the population. State the estimated distribution of P’. Construct a 92°o Confidence Interal for the true proportion of girls in the ages 8 to 12 beginning ice-skating classes at the ice Chalet.Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the ice Chalet. Assume that the children in the selected class are a random sample of the population. How much area is in both tails (combined)?Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the ice Chalet. Assume that the children in the selected class are a random sample of the population 87. How much area is in each tail?Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the ice Chalet. Assume that the children in the selected class are a random sample of the population Calculate the following: a. lower limit b. upper limit c. error bound Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the ice Chalet. Assume that the children in the selected class are a random sample of the population The 92% confidence interval is _______.Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population. 90. Fill In the blanks on the graph with the areas, upper and lower limits of the confidence Interval, and the sample proportion. Figure 8.10 Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population. In one complete sentence, explain what the interval means.Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population. Using the same p and level of confidence. suppose that n were increased to 100. Would the error bound become larger or smaller? How do you know?Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population. Using the same p’ and n=80, how would the error bound change if the confihence level were increased to 98%? Why?Use the following information to answer the next 16 exercises. The Ice Chalet offers dozens of different beginning ice- skating classes. All of the class names are put Into a bucket. The 5 P.M., Monday night, ages 8 to 12, beginning ice-skating class was picked. In the class were 6.1 girls and 16 boys. Suppose that we are Interested in the true proportion of gixls, ages 8 to 12. In all beginning ice-skating classes at the Ice Chalet. Assume that the children in the selected class are a random sample of the population. If you decreased the allowable error bound, why would the minimum sample size increase (keeping the same level of confidence)?Among various ethnic groups, the standard deviation of heights is known to be approximately three Inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. Forty -eight male Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation Is 2.8 inches. a.i. x ____ ii. ______ iii. n=______ b. In words, define the random variables X and X. c. Which distribution should you use for this problem? Explain your choice. d. Construct a 95% confidence interval for the population mean height of male Swedes. 1. State the confidence interval. U. Sketch the graph. UI. Calculate the error bound. e. What will happen to the level of confidence obtained if 1.000 male Swedes are surveyed instead of 48? Why?Announcements for 8.1 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 3.9.4 days, with a standard deviation of 1.28 days. Assume the underlying population Is normal. a. In words, define the random variables X and X. b. Which distribution should you use for this problem? Explain our choice. c. Construct a 95% confidence 1nteral for the population mean length of engineering conferences. I. State the confidence interval. U. Sketch the graph. lii. Calculate the error bound.Suppose that an accounting firm does a study to determine the time needed to complete one person’s tax forms. It randomly surveys 100 people. The sample mean Is 23.6 hours. There Is a known standard deviation of 7.0 hours. The population distribution Is assumed to be normal. a. i. x _____ ii. ______ iii. n=______ b. In words, define the random variables X and X . c. Which distribution should you use for this problem? Explain your choice. d. Construct a 90% confidence interval for the population mean time to complete the tax forms. i. State the confidence Interval. ii. Sketch the graph. iii. Calculate the error bound. e. If the firm wished to increase Its level of confidence and keep the error bound the same by taking another survey what changes should It make? f. If the firm did another survey, kept the error bound the same, and only surveyed 49 people, what would happen to the level of confidence? Why? g. Suppose that the firm decided that it needed to be at least 96% confident of the population mean length of time to within one hour. How would the number of people the firm surveys change? Why?A sample of 16 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights Is normal. The weight of each bag was then recorded. The mean weight was two ounces with a standard de1at1on of 0.12 ounces. The population standard deviation Is known to be 0.1 ounce. a. i. x =______ . ii. =______ iii. sx =______ . b. In words, define the random variable X. c. In words, define the random variable X . d. Which distribution should you use for this problem? Explain your choice. e. Construct a 90% confidence interval for the population mean weight of the candles. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. f. Construct a 98% confidence interval for the population mean weight of the candles. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. g. In complete sentences, explain why the confidence Interval In part f Is larger than the confidence interval in part e. h. In complete sentences, give an interpretation of what the interval in part f means.A camp director is interested in the mean number of letters each child sends during his or her camp session. The population standard deviation Is known to be 2.5. A survey of 20 campers is taken. The mean from the sample Is 7.9 with a sample standard deviation of 2.8. a. i. x =_____ ii. =_______ . iii. n=______ b. Define the random variables X and X .n words. c. Which distribution should you use for this problem? Explain your choice. d. Construct a 90% confidence Interval for the population mean number of letters campers send home. i. State the confidence Interval. ii. Sketch the graph. iii. Calculate the error bound. e. What will happen to the error bound and confidence interval if 500 campers are surveyed? Why?What Is meant by the tetm 90% confident when constructing a confidence interval for a mean? a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval. b. If we took repeated samples. apptoxlmately 90% of the confidence Intervals calculated from those samples would contain the sample mean. c. If we took repeated samples. appioximately 90% of the confidence Intervals calculated from those samples would contain the tnie value of the population mean. d. It we took repeated samples, the sample mean would equal the population mean In approximately 90% of the samples.The Federal Election Commission collects information about campaign contributions and disbursements for candidates and political committees each election cycle. During the 2012 campaign season, there were 1,619 candidates for the House of Representatives across the United States who received contributions from Individuals. Table 8.11 shows the total receipts from individuals for a random selection of .t0 House candidates rounded to the nearest 5100. The standard deviation for this data to the nearest hundred is = 5909,200. Table 8.11 a. Find the point estimate for the population mean. b. Using 95% confidence, calculate the error bound. c. Create a 95% confidence interval for the mean total individual contributions. d. Interpret the confidence interval in the context of the problem. $3,600 $1,243,900 $10,900 $385200 $581500 $7,400 $2,900 $400 $3,714.500 $632,500 $391.000 $467,400 $56.800 $5,800 $406,200 $733,200 $8000 $468,700 $75.200 $41,000 $13,300 $9500 $953,800 $1,113.500 $1,109.300 $353,900 $986,100 $88,600 $378200 $13,200 $3800 $745,100 $5,800 $3,072,100 $1,626,700 $512,900 $2.309,200 $6600 $202,400 $15,800 The American Community Survey (ACS), part of the United States Census Bureau, conducts a yearly census similar to the one taken every ten ears, but with a smaller percentage of participants. The most recent survey estimates with 90% confidence that the mean household income In the U.S. falls between $69,720 and 569,922. Find the point estimate for mean U.S. household Income and the error bound for mean U.S. household income.The average height of young adult males has a normal distribution with standard deviation of 2.5 Inches. You want to estimate the mean height of students at your college or university to within one inch with 93% confidence. How man male students must you measure?In six packages of The Flintstones Real Fruit Snacks there were five Barn-Barn snack pieces. The toal number of snack pieces in the six bags was 68. We wish to calculate a 96°o confidence interval for the population proportion of Barn-Barn snack pieces. a. Define the random variables X and P b. Which distribution should you use for this problem? Explain your choice c. Calculate p. d. Construct a 96% confIdence Interval for the population proportion of Barn-Barn snack pieces per bag. I. State the confidence Interval. II. Sketch the graph. Iii. Calculate the error bound. e. Do you think that six packages of fruit snacks yield enough data to give accurate results? Why or why not?A random survey of enrollment at 35 community colleges across the United States yielded the following figures: 6,414; 1,550; 2,109; 9,350; 21,828; 4,300; 5,944; 5,722; 2,825; 2,044: 5,481; 5,200; 5,853; 2,750; 10,012; 6,357; 27,000; 9,414; 7,681; 3,200; 17,500; 9,200; 7,380; 18,314; 6,557; 13,713; 17,768; 7,493; 2,771; 2,861; 1.263; 7,285; 28,165; 5.080; 11,622. Assume the underlying population is normal. a. i. x =______ ii. sx=_______. iii. n= ________ iv. n - 1= _________ b. Define the random variables X and X In words. C. Which distribution should you use for this problem? Explain your choice. d. Construct a 95% confidence Interval for the population mean enrollment at community colleges In the United States. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. e. What will happen to the error bound and confidence interval if 500 community colleges were surveyed? Why?Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is Interested In the mean amount of time individuals waste at the courthouse waiting to be called for Jury duty. The committee randomly surveyed 81 people who recently served as jurors. The sample mean wait time was eight hours with a sample standard deviation of four hours. a. i. x ______ ii. sx=_______ . iii. n _______ iv. n - 1 _________ b. Define the random variables X and X In words. c. Which distribution should you use for this problem? Explain your choice. d. Construct a 95% confidence interval for the population mean time wasted. i State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. e. Explain in a complete sentence what the confidence interval means.A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the dmg on a random sample of nine patients. The effective period of the tranquilizer for each patient (In hours) was as follows: 2.7; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. a. i. x ______ ii. sx=________ . iii. n _______ iv. n - 1 _________ b. Define the random variable X In words. c. Define the random variable X In words. d. Which distribution should you use for this problem? Explain your choice. e. Construct a 95°c confidence Interval for the population mean length of time. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. f. What does It mean to be ‘95% confident in this problem?Suppose that 14 children, who were learning to ride two-wheel bikes, were surveyed to determine how long they had to use training wheels. It was revealed that they used them an average of six months with a sample standard deviation of three months. Assume that the underlying population distribution is normal. a. 1 i. x ______ ii. sx=________ . iii. n _______ iv. n - 1 _________ b. Define the random variable X In worth. c. Define the random variable X in worth. d. Which distribution should you use for this problem? Explain you choice. e. Construct a 99°o confidence interval for the population mean length of time using training wheels. i. State the confidence Interval. ii. Sketch the graph. iii. Calculate the error bound. f. Why would the error bound change if the confidence level were lowered to 90%?The Federal Election Commission (FEC) collects Information about campaign contributions and disbursements for candidates and political cornrnlnees each election cycle. A political action committee (PAC) Is a committee formed to raise money for candidates and campaigns. A Leadership PAC Is a PAC formed by a federal politician (senator or representative) to raise money to help other candidates’ campaigps. The FEC has teported financial information for 556 Leadership PACs that operating during the 2011—2012 election cycle. The following table shows the total receipts during this cycle for a random selection of 30 Leadership PACs. Table 8.12 = $251. 854.23 s= $521. 130.41 Use this sample data to construct a 96% confidence interval for the mean amount of money raised by all Leadership PACs during the 2011—20 12 election cycle. Use the Student’s t-distrlbutlon. $46.500.00 $0 $40,966.50 $105,887.20 $5175.00 $29,050.00 $19,500.00 $181,557.20 $31,500.00 $149,970.80 $2.555.363.20 $12025.00 $409,000.00 $60521.70 $18,000.00 $61,810.20 $76,530.80 $119459.20 $0 $63,520.00 $6,500.00 $502,578.00 $705061.10 $708,258.90 $135,810.00 $2,000.00 $2,000.00 $0 $1,287,933.80 $219148.30 Forbes magazine published data on the best small finns in 2012. These were finns that had been publicly traded for at least a veaz, have a stock price of at least 55 per share, and have reported annual revenue between 55 million and Si, billion. The Table 8.13 shows the ages of the corporate CEOs for a random sample of these firms. 48 58 51 61 56 59 74 63 53 50 59 60 60 57 55 63 57 47 55 57 43 61 62 49 67 67 55 55 49 Table 8.13 Use this sample data to consuua a 90% confidence interval for the mean age of CEOs for these top small flims. Use the Student’s t-distribution.Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is .1.1 seats. a. i. x ______ ii. sx=_______ . iii. n _______ iv. n - 1 _________ b. Define the random variables X and X In words. c. Which distribution should you use for this problem? Explain your choice. d. Construct a 92% confidence interval for the population mean number of unoccupied seats per flight. i. State the confidence interval. ii. Sketch the graph. lii. Calculate the error bound.In a recent sample of 84 used car sales costs, the sample mean was $6425 with a standard deviation of $3,156. Assume the underlying distribution Is approximately normal. a. Which distribution should you use for this problem? Explain your choice. b. Define the random variable X in words. c. Construct a 95°b confidence interval for the population mean cost of a used car. i. State the confidence Interval. ii. Sketch the graph. iii. Calculate the error bound. d. Explain what a “95% confidence interval” means for this study.Six different national brands of chocolate chip cookies were randomly selected at the supermarket. The grams of fat per serving are as follows: 8; 8; 10; 7; 9; 9. Assume the underlying distribution Is approximately normal. a. Construct a 90% confidence interval for the population mean grams of fat per serving of chocolate chip cookies sold in supermarkets. i. State the confidence Interval. ii. Sketch the graph. iii. Calculate the error bound. b. If you wanted a smaller error bound while keeping the same level of confidence, what should have been changed in the study before It was done? c. Go to the store and record the grams of fat per serving of six brands of chocolate chip cookies. d. Calculate the mean. e. Is the mean within the Interval you calculated in part a? Did you expect ft to be? Why or why not?A survey of the mean number of cents off that coupons give was conducted by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News. The following data were collected: 20¢; 75¢; 50¢: 65¢; 30¢; 55¢; 40¢; 40¢; 30¢; 55¢; 1.50¢; .10¢; 65¢; 40¢. Assume the underlying distribution is approximately normal. a. i. x ______ ii. sx=_______ . iii. n _______ iv. n - 1 _________ b. Define the random variables X and X hi words. c. Which distribution should you use for this problem? Explain your choice. d. Construct a 95% confidence Interval for the population mean worth of coupons. i. State the confidence interval. ii Sketch the graph. iii. Calculate the error bound. e. If many random samples were taken of size 14, what percent of the confidence intervals constructed should contain the population mean worth of coupons? Explain why.Use the following information o ansier the next two exeirises: A quality control specialist for a restaurant chain takes a random sample of size 12 to check the amount of soda served in the 16 oz. serving size. The sample mean Is 13.30 isith a sample standard deviation of 1.55. Assume the underlying population Is normally distributed. 115. Find the 95% Confidence Interval for the true population mean for the amount of soda served. a. (12.42, 14.18) b. (12.32, 14.29) c. (12.50, 14.10) d. Impossible to determine Use the following information o ansier the next two exeirises: A quality control specialist for a restaurant chain takes a random sample of size 12 to check the amount of soda served in the 16 oz. serving size. The sample mean Is 13.30 isith a sample standard deviation of 1.55. Assume the underlying population Is normally distributed 116. That is the error bound? a. 0.87 b. 1.98 c. 0.99 d. 1.74 Insurance companies are interested In knowing the population percent of drivers who always buckle up before riding In a car. a. When designing a study to determine this population proportion, what Is the minimum number you would need to survey to be 95% confident that the population proportion Is estimated to within 0.03? b. If It were later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Why?Suppose that the insurance companies did do a survey. They randomly surveyed 400 drivers and found that 320 claimed they always buckle up. We are Interested in the population proportion of drivers who claim they always buckle up. a. i. x ______ ii. n=______ . iii. P’ _______ b. Define the random variables X and P. in words. c. Which distribution should you use for this problem? Explain your choice. d. Construct a 95°o confidence interval for the population proportion who claim they always buckle up. i. State the confidence Interval. ii. Sketch the graph. iii. Calculate the error bound. e. If this survey were done by telephone, list three difficulties the companies might have in obtaining random results.According to a recent survey of 1,200 people. 61% feel that the president Is doing an acceptable job. We are interested in the population proportion of people who feel the president is doing an acceptable job. a. Define the random variables X and P’ In words. b. Which distribution should you use for this problem? Explain your choice. c. Construct a 90% confidence Interval for the population proportion of people who feel the president is doing an acceptable job. i. State the confidence Interval. ii. Sketch the graph. iii. Calculate the en-or bound.An article regarding interracial dating and marriage recently appeared In the Washington Post. Of the 1,709 randomly selected adults, 315 identified themselves as Latinos, 323 identified themselves as blacks. 25.1 identified themselves as Asians, and 779 identified themselves as whites. In this survey, 86% of blacks said that they would welcome a white person into their families. Among Asians, 77% would welcome a white person into their families. 71% would welcome a Latino, and 66% would welcome a black person. a. W are interested in finding the 95% confidence Interval for the percent of all black adults who would welcome a white person into their families. Define the random variables X and P. In words. b. Which distribution should you use for this problem? Explain your choice. c. Construct a 95% confidence Interval. i. State the confidence Interval. ii. Sketch the graph. iii. Calculate the error bound.Refer to the information In Exercise 8.120. a. Construct three 95% confidence intervals. 1. percent of all Asians who would welcome a white person Into their families. ii. percent of all Asians who would welcome a Latino Into their families. ií. pet cent of all Asians who would welcome a black person into their families. b. Even though the three point estimates are different, do any of the confidence intervals overlap? Which? c. For any Intervals that do overlap. In words, what does this imply about the significance of the differences in the true proportions? d. For any Intervals that do not overlap. In words, what does this Imply about the significance of the differences In the true proportions?Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study 1.5% of the 451 members of the 50-Plus Fitness Association died. We are interested In the proportion of people over 50 who ran and died in the same eight-year period. a. Define the random variables X and P in words. b. Which distribution should you use for this problem? Explain your choice. c. Construct a 97% confidence interval for the population proportion of people over 50 who ran and died in the same eight—year period. i. State the confidence Interval. ii. Sketch the graph. iii. Calculate the error bound. d. Explain what a 97% confidence interval means for this study.A telephone poll of 1,000 adult Americans was reported in an issue of Time Magazine. One of the questions asked was “What Is the main problem facing the country? Twenty percent answered ‘crime.” We are Interested In the population proportion of adult Americans who feel that crime is the main problem. a. Define the random variables X and P in words. b. Which distribution should you use for this problem? Explain your choice. c. Construct a 95% confidence interval for the population proportion of adult Americans who feel that crime Is the main problem. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. d. Suppose we want to lower the sampling error. What is one way to accomplish that? e. The sampling error given by Yankelovich Partners, Inc. (which conducted the poll) Is ±3%. In one to three complete sentences, explain what the ±3% represents.Refer to Exercise 8.123. Another question in the poll was (How much are] you worried about the quality of education in our schools?’ Sixty-three percent responded a lot. We are Interested In the population proportion of adult Ameitcans who are worried a lot about the quality of education in our schools. a. Define the random variables X and P In words. b. Which disutribution should you use f or this problem? Explain your choice. c. Construct a 95% confidence interval for the population propc*tIon of adult Americans who are wonted a lot about the quahtv of education in our schools. 1. State the confidence interval. 11. Sketch the giaph. ill. Calculate the error bound. d. The sampling error given by Yankelovich Partners, Inc. (which conducted the poll) Is 3%. In one to three complete sentences, explain what the 3% represents.Use the following informariton to answer the next three exercises: According to a Field Poll, 79% of California adults (actual results are 400 out of 506 SUfl eyed) feel that education and our schools Is one of the top issues facing California. We wish to constnict a 90% confidence Interval for the tnae proportion of California adults who feel that education and the schools is one of the top issues facing California. A point estimate for the true population proportion is: a. 0.90 b. 1.27 c. 0.79 d. -100 Use the following informariton to answer the next three exercises: According to a Field Poll, 79% of California adults (actual results are 400 out of 506 SUfl eyed) feel that education and our schools Is one of the top issues facing California. We wish to constnict a 90% confidence Interval for the tnae proportion of California adults who feel that education and the schools is one of the top issues facing California. A 90% confidence interval for the population proportion is a. (0.761, 0.820) b. (0.125,0.188) c. (0.755, 0.826) d. (0.130, 0.183)Use the following informariton to answer the next three exercises: According to a Field Poll, 79% of California adults (actual results are 400 out of 506 SUfl eyed) feel that education and our schools Is one of the top issues facing California. We wish to constnict a 90% confidence Interval for the tnae proportion of California adults who feel that education and the schools is one of the top issues facing California. 127. The enor bound is approxi.matelv a. 1.581 b. 0.791 c. 0.059 d. 0.030 Use the following information to answer the next v exercises Five hundred and eleven (511) homes in a certain southern California communcv are randomly surveyed to determine if they meet minimal earthquake preparedness recommendations. One hundred seventy-three (173) of the homes suzveved met the minimum recommendations for earthquake preparedness, and 338 did not. 128. Find the confidence interval at the 900 Confidence Level for the true population proportion of southern California community homes meeting at least the minimum recommendations fo earthquake preparedness. a. (02975. 0.3796) b. (0.6270. 0.6959) C. (0.3041. 0.3730) d. (0.6204. 0.7025)Use the following information to answer the next v exercises Five hundred and eleven (511) homes in a certain southern California community are randomly surveyed to determine if they meet minimal earthquake preparedness recommendations. One hundred seventy-three (173) of the homes suzveyed met the minimum recommendations for earthquake preparedness, and 338 did not. 129. The point estimate for the population proportion of homes that do not meet the minimum recommendations for earthquake preparedness is ______ a. 0.6614 b. 0.3386 173 d. 338 On May 23, 2013, Gallup reported that of the 1,005 people surveyed. 76% of U.S. workers believe that they will continue wotidng past tetliement age. The confidence level for this study was reported at 95% wIth a 3% mat gin of error. a. Determine the estimated proportion from the sample. b. Determine the sample size. c. Identif CL and a. d. Calculate the error bound based on the Information provided. e. Compare the error bound In part d to the margin of error reported by Gallup. Explain any differences between the values. f. Create a confidence Interval for the results of this study. g. A reporter is covering the release of this study for a local neiss station. How should she explain the confidence interval to her audience?A national survey of 1000 adults was conducted on May 13. 2013 by Rasmussen Reports. ft concluded with 95% confidence that 49% to 55% of Americans believe that big-rime college sports programs corrupt the process of higher education. a. Find the point estimate and the error bound for this confidence Interval. b. Can we (with 95% confidence) conclude that more than half of all American adults believe this? c. Use the point estimate from part a and n 1.000 to calculate a 75% confidence Interval for the proportion of American adults that believe that major college sports programs conupt higher education. d. Can we (with 75% confidence) conclude that at least half of all American adults believe this?Public Policy Polling recently conducted a survey asking adults across the U.S. about music preferences. When asked, 80 of the 571, participants admitted that they have illegally downloaded music. a. Create a 99% confidence Irnerval for the tnie proportion of American adults who have Illegally downloaded music. b. This survey was conducted through automated telephone Interviews on May 6 and 7. 2013. The error bound of the survey compensates for sampling enor, or natural vajlabllltv among samples. List some factors that could affect the suive s outcome that are no covered b the margin of error. c. Without perfotming any calculations, describe how the confidence interval would change If the confidence level changed from 990 1090%.You plan to conduct a survey on your college campus to learn about the political awareness of students. You want to estimate the tnie proportion of college students on your campus who voted in the 2012 presidential election with 95% confidence and a margin of error no greater than five percent. How many students must you interview?In a recent Zogby International Poll, nine of .18 respondents rated the likelihood of a tenorlst attack In their communit as ‘likely” or “very likely.‘ Use the p1us four method o create a 97% confidence Interval for the proportion of American adults who believe that a terrorist attack In their community is likely or very likely. Explain what this confidence Interval means in the context of the problem.A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill In the correct symbol (=,,,,,) for the null and alternative hypotheses. a. H0:_66 b. H0:_66 We want to test If It takes fewer than 45 minutes (0 teach a lesson plan. State the null and alternative hypotheses. Fill In the correct symbol (=,,,,,) for the null and alternative hypotheses. a. H0: _45 b. H0:_15 On a state drivers test. about .10% pass the test on the first a We want to test if more than .10% pass on the first try. Fill in the correct symbol (, x. , <, . >) for the null and alternative hypotheses. a. Ho:p_O.40 b. Ha:p_O.40 Suppose the null hypothesis, H0, Is: the blood cultures contain no traces of pathogen X. State the I Type I and Type II errors.Suppose the null hypothesis. H0. Is: a patient is not sick. Which type of error has the greater consequence, 1pe I or Type II?“Red tide” is a bloom of poison-producing algae—a few different species of a class of plankton called dinoflagellates. When the weather and water conditions cause these blooms, shellfish such as clams living In the area develop dangerous levels of a paralysis-inducing toxin. In Massachusetts. the Division of Marine Fisheries (DMF) monitors levels of the toxin in shellfish by regular sampling of shellfish along the coastline. If the mean level of toxin in clams exceeds 800 pg (micrograms) of toxin per kg of clam meat In any area, clam harvesting Is banned there until the bloom Is over and levels of toxin in clams subside. Describe both a Type I and a Type II error In this context, and state which error has the greater consequence.Determine both Type I and Type II errors for the following scenario: Assume a null hypothesis, H0. that states the percentage of adults with jobs Is at least 88%. Identify the Type I and Type II errors from these four statements. a. Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88% when that percentage is actually less than 88% b. Not to reject the null hypothesis that the percentage of adults who have jobs is at least 88% when the percentage is actually at least 88%. c. Reject the null hypothesis that the percentage of adults who have jobs is at least 88% when the percentage is actually at least 88%. d. Reject the null hypothesis that the percentage of adults who have jobs is at least 88% when that percentage is actually less than 88%.A normal distribution has a standard deviation of 1. We want to verify a claim that the mean Is greater than 12. A sample of 36 Is taken with a sample mean of 12.5. H0:12 H0:>12 The p-value Is 0.00.3 Draw a graph that shows the p-value.Its a Boy Genetics Labs claim their procedures improve the chances of a boy being born. The results for a test of a single population proportion are as follows: H0:p 0.50, H0:p > 0.50 a=0.0l p-value 0.025 Interpret the results and state a conclusion In simple, non-technical terms.H0:=10, H0:< 10 Assume the p-value is 0.0935. What type of test is this? Draw the picture of the p-value.H0:1,Ha:1 Assume the p-value is 0.1243. What type of test is this? Draw the picture of the p-value.H0:p=0.5,Ha:p0.5 Assume the p-value is 0.2564. What type of test is this? Draw the picture of the p-value.The mean throwing distance of a football for Marco, a high school freshman quarterback, is 40 yards, with a standard deviation of two yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 20 throws. For the 20 throws, Marcos mean distance was 45 yards. The coach thought the different grip helped Marco throw farther than 40 yards. Conduct a hypothesis test using a preset a = 0.05. Assume the throw distances for footballs are normal. First, determine what type of test this Is, set up the hypothesis test, find the p-value, sketch the graph, and state your conclusion. [} Using the T1-83, 83+. 84, 84+ Calculator Press STAT and arrow over to TESTS. Press l:Z-Test. Arrow over to Stats and press ENTER. Arrow down and enter 40 for p0 (null hypothesis), 2 for a. 45 for the sample mean, and 20 for n. Arrow down to p: (alternative hypothesis) and set it either as <, or >.. Press ENTER. Arrow down to Calculate and press ENTER. The calculator not only calculates the p-value but ft also calculates the test statistic (z-score) for the sample mean. Select <, or > for the alternative hypothesis. Do this set of instructions again except arrow to Draw (instead of Calculate). Press ENTER. A shaded graph appears with test statistic and p-value. Make sure when you use Draw that no other equations are highlighted In Y = and the plots are turned off.It is believed that a stock price for a particular company will grow at a rate of 55 per week with a standard deviation of Si. An Investor believes the stock won’t grow as quickly. The changes in stock price is recorded for ten weeks and are as follows: $4, $3, $2, $3, $1, $7, $2, $1, $1, $2. Perform a hypothesis test using a 5% level of significance. State the null and alternative hypotheses, find the p-value, state your conclusion, and identify the Type I and Type II errors.A teacher believes that 85% of students in the class will want to go on a field trip to the local zoo. She performs a hypothesis test to determine If the percentage is the same or different from 85%. The teacher samples 50 students and 39 reply that they would want to go to the zoo. For the hypothesis rest, use a 1% level of significance. First. determine what type of test this Is, set up the hypothesis test, find the p-value, sketch the graph, and state your conclusion.Marketers believe that 92% of adults In the United States own a cell phone. A cell phone manufacturer believes the number is actually lower. 200 American adults axe surveyed, of which, 174 report having cell phones. Use a 5% level of significance. State the null and alternative hypothesis, find the p-value, state your conclusion, and identify the Type I and Type II errors.You are testing that the mean speed of your cable Internet connection Is more than three Megabits per second. What is the random variable? Describe In words.You ate testing that the mean speed of your cable Internet connection is more than three Megabits per second. State the null and alternative hypotheses.The American family has an average of two children. What is the random variable? Describe in words.The mean entry level salary of an employee at a company is $58.000. You believe it Is hIg1er for IT professionals in the company. State the null and alternative hypotheses.A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area Is 0.83. You want to test to see If the proportion is aauafly less. What is the random variable? Describe In words.A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the claim is coned. State the null and alternative hypotheses.In a population of fish approximately 42% are female. A test is conducted to see if. in fact, the proportion Is less. State the null and alternative hypotheses.Suppose that a recent article stated that the mean time spent In jail by a first—time convicted burglar Is 2.5 years. A study was then done to see If the mean time has Increased In the new cannon A random sample of 26 first-time convicted burglars In a recent year was picked. The mean Length of time In jail from the survey was 3 years with a standard deviation of 1.8 years. Suppose that It Is somehow known that the population standard deviation Is 1.5. If you were conducting a hypothesis test to deteimine if the mean length of jail time has Increased, what would the null and alternative hypotheses be? The distribution of the population is normal. a. H0: b. H: _______A random survey of 75 death row Inmates revealed that the mean length of time on death row Is 17.4 years with a standard deviation of 6.3 years. If you were conducting a hypothesis test to determine if the population mean time on death row could likely be 15 years, what would the null and alhternative hypotheses be? a. H0: b. H3: _________The National Institute of Mental Health published an article stating that In any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive Illness. Suppose that in a survey of 100 people In a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive Illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be? a. H0: b. H0:The mean price of mid-sized cars In a region is $32,000. A test is conducted to see if the claim is true. State the Type I and Type II errors in complete sentences.A sleeping bag Is rested to withstand temperatures of —15 °F. You think the bag cannot stand temperatures that low. State the Type I and Type II errors in complete sentences.For Exercise 9.12, what are and in words?In words, describe 1— 3For Exercise 9.12.A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, H0, is: the surgical procedure will go well. State the Type I and Type II errors in complete sentences.A group of doctors is deciding whether or not to perform an operation. Suppose the null hypothesis, H0, is: the surgical procedure will go well. Which is the error with the greater consequence?The power of a test is 0.981. What is the probability of a Type II error?A group of divers is exploring an old sunken ship. Suppose the null hypothesis. H0, Is: the sunken ship does not contain buried treasure. State the Type I and Type II errors In complete sentences.A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis. H0. is: the sample does not contain E-coil. The probability that the sample does not contain E-coll, but the microbiologist thinks it does is 0.012. The probability that the sample does contain E-coil, but the microbiologist thinks it does not is 0.002. What Is the power of this test?A microbiologist is testing a water sample for E-coli. Suppose the null hypothesis, H0, is: the sample contains E-coli. Which is the error with the greater consequence?Which two distributions can you use for hypothesis testing for this chapter?Which distribution do you use when you are testing a population mean and the population standard deviation is known? Assume a normal disthbution, with n >30.Which distribution do you use when the standard deviation is not known and you are testing one population mean? Assume sample size is large.A population mean Is 13. The sample mean is 12.8. and the sample standard deviation is two. The sample size is 20. What distribution should you use to perform a hypothesis test? Assume the underlying population is normal.A population has a mean is 25 and a standard deviation of five. The sample mean Is 24, and the sample size is 108. What distribution should you use to perform a hypothesis test?It Is thought that .12% of respondents in a taste test would prefer Brand A. In a particular test of 100 people, 39% preferred Brand A. ‘What distribution should you use to perform a hypothesis test?You ate performing a hypothesis test of a single population mean using a Students t-distribution. What must you assume about the distribution of the data?You are performing a hypothesis test of a single population mean using a Students t-distribution. The data are not from a simple random sample. Can you accurately perform the hypothesis test?You are performing a hypothesis test of a single population proportion. What must be true about the quantities of np and nq?You are performing a hypothesis test of a single population proportion. You find out that np is less than five. ‘bat must you do to be able to perform a valid hypothesis test?You are peform1ng a hypothesis test of a single population proportion. The data come from which distribution?When do you reject the null hypothesis?The probability of winning the grand prize at a particular carnival game is 0.005. Is the outcome of winning very likely or very unlikely?The probability of winning the grand prize at a particular carnival game is 0.005. Michele wins the grand prize. Is this considered a rare or common event? why?It is believed that the mean height of high school students who play basketball on the school team is 73 inches with a standard deviation of 1.8 inches. A random sample of .10 players Is chosen. The sample mean was 71 inches. and the sample standard deviation was 1.5 years. Do the data suppo1 the claim that the mean height Is less than 73 inches? The p-value is almost zero. State the null and alternative hypotheses and interpret the p-value.The mean age of graduate students at a University is at most 31 y ears with a standard deviation of two years. A random sample of 15 graduate students Is taken. The sample mean is 32 years and the sample standard deviation is three years. Are the data significant at the 1% level? The p-value is 0.0264. State the null and alternative hypotheses and interpret the p-value.Does the shaded region represent a low or a high p-value compared to a level of significance of 1%? Figure 9.24 What should you do when a >p-value?What should you do if a = p-value?If you do not reject the null hypothesis, then it must be true. Is this statement correct? State why or why not in complete sentences.Use the blowing information to answer the next seen exeircises: Suppose that a recent article stated that the mean time spent In Jail by a first-time convicted burglar Is 2.5 years. A study was then done to see If the mean time has increased In the new century. A random samp’e of 26 first-time convicted burglars In a recent year was picked. The mean length of time In Jail from the survey was three years with a standard deviation of 1.8 years. Suppose that It Is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to deteimine If the mean length of jail time has increased. Assume the distribution of the Jail times Is approximately normal. Is this a test of means or proportions?Use the blowing information to answer the next seen exeircises: Suppose that a recent article stated that the mean time spent In Jail by a first-time convicted burglar Is 2.5 years. A study was then done to see If the mean time has increased In the new century. A random samp’e of 26 first-time convicted burglars In a recent year was picked. The mean length of time In Jail from the survey was three years with a standard deviation of 1.8 years. Suppose that It Is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to deteimine If the mean length of jail time has increased. Assume the distribution of the Jail times Is approximately normal. What symbol represents the random variable for this test?Use the blowing information to answer the next seen exeircises: Suppose that a recent article stated that the mean time spent In Jail by a first-time convicted burglar Is 2.5 years. A study was then done to see If the mean time has increased In the new century. A random samp’e of 26 first-time convicted burglars In a recent year was picked. The mean length of time In Jail from the survey was three years with a standard deviation of 1.8 years. Suppose that It Is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to deteimine If the mean length of jail time has increased. Assume the distribution of the Jail times Is approximately normal. 43. In words, define the random variable for this test.Use the blowing information to answer the next seen exeircises: Suppose that a recent article stated that the mean time spent In Jail by a first-time convicted burglar Is 2.5 years. A study was then done to see If the mean time has increased In the new century. A random samp’e of 26 first-time convicted burglars In a recent year was picked. The mean length of time In Jail from the survey was three years with a standard deviation of 1.8 years. Suppose that It Is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to deteimine If the mean length of jail time has increased. Assume the distribution of the Jail times Is approximately normal. Is known and, if so, what is it?Use the blowing information to answer the next seen exercises: Suppose that a recent article stated that the mean time spent In Jail by a first-time convicted burglar Is 2.5 years. A study was then done to see If the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time In Jail from the survey was three years with a standard deviation of 1.8 years. Suppose that It is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to determine If the mean length of jail time has increased. Assume the distribution of the Jail times Is approximately normal. 45. Calculate the following: a. x ____________. b. ____ C. Sx___ d. n _______Use the blowing information to answer the next seen exeircises: Suppose that a recent article stated that the mean time spent In Jail by a first-time convicted burglar Is 2.5 years. A study was then done to see If the mean time has increased In the new century. A random samp’e of 26 first-time convicted burglars In a recent year was picked. The mean length of time In Jail from the survey was three years with a standard deviation of 1.8 years. Suppose that It Is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to deteimine If the mean length of jail time has increased. Assume the distribution of the Jail times Is approximately normal. Since both and sx, are given, which should be used? In one to two complete sentences, explain why.Use the blowing information to answer the next seen exeircises: Suppose that a recent article stated that the mean time spent In Jail by a first-time convicted burglar Is 2.5 years. A study was then done to see If the mean time has increased In the new century. A random samp’e of 26 first-time convicted burglars In a recent year was picked. The mean length of time In Jail from the survey was three years with a standard deviation of 1.8 years. Suppose that It Is somehow known that the population standard deviation is 1.5. Conduct a hypothesis test to deteimine If the mean length of jail time has increased. Assume the distribution of the Jail times Is approximately normal. 47. State the distribution to use for the hypothesis test.A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. Conduct a hypothesis test to determine If the population mean time on death row could likely be 15 years. a. Is this a test of one mean or proportion? b. State the null and alternative hypotheses. H0:________ Ha :_________ . c. Is this a right-called, left-tailed, or two-tailed rest? d. What symbol represents the random variable for this test? e. In words, define the random variable for this test. f. Is the population standard deviation known and. if so, what Is It? g. Calculate the following: i. x ____________ ii s= _______ . iii. n _________ h. Which test should be used? I. State the distribution to use for the hypothesis test. j. Find the p-value. k. At a pre-conceived a = 0.05. what Is your: i. Decision: ii. Reason for the decision: iii. Conclusion (write out in a complete sentence):Assume H0: = 9 and H0:< 9. Is this a left-tailed, light-tailed, or two-tailed test?Assume H0:6 and H0: > 6. Is this a left-tailed, light-tailed, or two-tailed test?Assume H0: p = 0.25 and Ha: p 0.25. Is this a left-tailed, right-tailed, or two-tailed test?Draw the general graph of a left-tailed test.Draw the graph of a two-tailed test.A bottle of water Is labeled as containing 16 fluid ounces of water. You believe it Is less than that. What type of test would you use?Your friend claims that his mean golf score Is 63. You want to show that it Is higher than that. What type of test would you use?A bathroom scale claims to be able to dentify correctly any weight within a pound. You think that It cannot be that accurate. What type of test would you use?You flip a coin and record whether it shows heads or tails. You know the probability of getting heads is 50%, but you think it is less for this particular coin. What type of test would you use?If the alternative hypothesis has a not equals ( ) symbol, you know to use which type of test?Assume the null hypothesis states that the mean is at least 18. Is this a left-tailed, right-tailed, or two-tailed test?Assume the null hypothesis states that the mean is at most 12. Is this a left-tailed, right-tailed, or two-tailed test?Assume the null hypothesis states that the mean Is equal to 88. The alternative hypothesis states that the mean is not equal to 88. Is this a left-tailed, right-tailed, or two-tailed test?Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis. H0. in terms of the appropriate parameter (p or p). a. The mean number of years Americans work before retiring Is 34. b. At most 60°o of Americans vote in presidential elections. c. The mean starting salary for San Jose State University graduates is at least S100.000 per year. d. Twenty-nine percent of high school seniors get drunk each month. e. Fewer than 5% of adults ride the bus to work in Los Angeles. f. The mean number of cars a person owns in her lifetime is not more than ten. g. About half of Americans prefer to live awa from cities, given the choice. h. Europeans have a mean paid vacation each year of six weeks. I. The chance of developing breast cancer is under 11% for women. j. Private universities’ mean tuition cost Is more than S20,000 per year.Over the past few decades, public health officials have examined the link between weight concerns and teen girLs’ smoking. Reseaichers surve ed a group of 273 randomly selected teen girls living In Massachusetts (between 12 and 15 ears old). After four years the girls were surveyed again. Stxtvthree said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? The alternative hypothesis is: a. P0.30 b. p0.30C. p0.30d. p>0.30 A statistics instructor believes that fewer than 20% of Evergjeen Valle College (EVC) students attended the opening night midnight showing of the latest Hanv Potter movie. She surve s 84 of her students and finds that 11 attended the midnight showing. An appropriate alternative hypothesis Is: a. p=0.20 b. p>0.20 C. p<0.20 d. p0.20 Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are: a. H0:x = 4.5, Ha:x > 4.5 b. H0:4.5 , Ha:<4.5 C. H0: = 4.75, Ha: > .1.75 d. H0: = 4.5, Ha:>4.5 State the Type I and Type II errors in complete sentences given the following statements. a. The mean number of years Americans work before retiring Is 34. b. At most 60°o of Americans vote in presidential elections. c. The mean starting salary for San Jose State Universit graduates is at least $100,000 per veal. d. Twenty-nine percent of high school seniors get drunk each month. e. Fewer than 5% of adults ride the bus to work In Los Angeles. f. The mean number of cars a person owns In his or her lifetime Is not more than ten. g. About half of Americans prefer to live away from cities, given the choice. h. Europeans have a mean paid vacation each year of six weeks. 1. The chance of developing breast cancer Is under 1100 for women. j. Private universities mean tuition cost is more than $20,000 per ‘ear.For statements a-j in Exercise 9.109. answer the following in complete sentences. a. State a consequence of committing a Type I error. b. State a consequence of committing a Type II error.When a new drug is created. the pharmaceutical company must subject ft to testing before receiving the necessary permission from the Food and Drug Administration (FDA) to market the drug. Suppose the null hypothesis Is “the drug Is unsafe.’ What Is the Type H Error? a. To conclude the drug is safe when in, fact, It Is unsafe. b. Not to conclude the drug Is safe when, in fact, It Is safe. c. To conclude the drug is safe when, In fact, It Is safe. d. Not to conclude the drug Is unsafe when, in fact, it Is unsafe.A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening midnight showing of the latest Hart Potter movie. She surve s 8-I of her students and finds that 11 of them attended the midnight showing. The Tpe I ertor Is to conclude that the percent of EVC students who attended Is ________ a. at least 200ô, when In fact, It Is less than 20%. b. 20%, when In fact. It Is 20%.. c. less than 20%, when In fact, it is at least 20%. d. less than 20%, when In fact, It is Less than 20%.It Is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intennedlae Algebra students get less than seven hours of sleep per night, on average? The Type II error Is not to reject that the mean number of hours of sleep LTCC students get per night Is at least seven when, In fact, the mean number of hours a. is more than seven hours. b. is at most seven hours. c. is at least seven hours. d. Is less than seven hours.Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization chinks that, cunenth the mean is higher. Fifteen randomly chosen teenagers were asked how many bows per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. the Type I enor Is: a. to conclude that the cunent mean hours per week Is higher than 4.5, when In fact. It Is higher b. to conclude that the current mean bouts per week Is higher than 4.5, when in fact, it is the same c. to conclude that the mean hours per week currently Is 4.5, when In fact. It Is higher d. to conclude that the mean hours per week currently Is no higher than .1.5, when In fact, It Is not higher It Is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 50, do LTCC intermediate Algebra students get less than seven hours of sleep per night, on average? The distribution to be used for this test is X _______________ a. N(7.24,1.93 22) b. N(7.24. 1.93) c. t22 d. t21 The National Institute of Mental Health published an article stating that In any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that In a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine If the true proportion of people In that town suffering from depression or a depressive illness Is lower than the percent in the general adult American population. a. Is this a test of one mean or proportion? b. State the null and alternative hypotheses. H0:___________ Ha:___________ . c. Is this a right-tailed, left-tailed, or two-tailed test? d. What symbol represents the random variable for this test? e. In words, define the random variable for this test. f. Calculate the following: i. x= _____________ ii n= ____________ iii. p’ = ____________ g. Calculate = ________. Show the formula set-up. h. State the distribution to use for the hypothesis test. 1. Find the p-value. j. At a pie-conceived a 0.05. what Is your: i. Decision: ii. Reason for the decision: iii. Conclusion (write out in a complete sentence):A particular brand of tires claims that its deluxe tire averages at least 50000 miles before It needs to be replaced. From pas studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design Is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9800 miles. Using alpha = 0.05, Is the data highly Inconsistent with the claim?From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant of around 2.1 years. A survey of .10 smokers of this generation was done to see if the mean starting age Is at Least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?The cost of a daily newspaper varies from city to city However, the variation among prices remains steady with a standard deviation of 20C. A study was done to test the claim that the mean cost of a daily newspaper is $1.00. Twelve costs yield a mean cost of 95C with a standard deviation of 18C. Do the data support the claim at the 1% level?An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of .49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the 1% level?The mean number of sick days an employee takes per year is believed to be about ten. Members of a personnel department do not believe this figure. They randomly survey eight employees. The number of sick days they took for the past ear are as follows: 12; 4; 15; 3; 11: 8; 6; 8. Let x the number of sick days they took for the past year. Should the personnel team believe that the mean number is ten?In 1955, Life Magazine reported that the 25 year-old mother of three worked, on average, an 80 hour week. Recently, many groups have been studying whether or no the women’s movement has, In fact, resulted In an Increase In the average work week for women (combining employment and at-home work). Suppose a stud was done to determine If the mean work week has Increased. 81 women were surveyed with the following resuks. The sample mean was 83; the sample standard deviation was ten. Does It appear that the mean work week has Increased for women at the 5% level?Your sta1stIcs Instructor claims that 60 percent of the students who rake her Elementar Statistics class go through life feeling more enriched. For some reason that she canr quite figure out, most people dont believe her. You decide to check this out on your own. You randomly survey 64 of her past Elementary Statistics students and find that 3-I feel more enriched as a result of her class. Now, what do you think?A Nissan Motor Corporation advertisement read, The average mans LQ. is 107. The average brown trouts I.Q. 154. So why cant man catch brown trout?’ Suppose you believe that the brown trouts mean I.Q. is greater than four. You catch 12 brown trout. A fish psychologLst determines the I.Q.s as follows: 5; 4; 7; 3; 6; 4; 5; 3; 6; 3; 8; 5. Conduct a hypothesis test of your belief.Refer to Exercise 9.19. Conduct a hypothesis test to see if your decision and conclusion would change if your belief were that the brown trour’s mean I.Q. is not four.According to an article in Newsweek, the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100: 114 (46.7% girls). Suppose you don’t believe the reported figures of the percent of girls born In China. You conduct a swd In this study, you count the number of girls and boys born In 150 randomly chosen recent births. There are 60 girls and 90 boys born of the 150. Based on your study, do you believe that the percent of girls born in China is .16.7?A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel. A contingent doubts that the percent Is really that high. It conducts Its own surve. Out of 76 Americans surveyed, only two had seen or sensed the presence of an angel. As a result of the contingent’s survei, would you agree with the Newsweek poll? In complete sentences, also give three reasons why the two polls might give different results.The mean work week for engineers In a start-up company is believed to be about 60 hours. A newly hired engineer hopes that it’s shorter. She asks ten engineering friends in start-ups for the lengths of their mean work weeks. Based on the results that follow, should she count on the mean work week to be shorter than 60 hours? Data (length of mean work week): 70; 45; 55; 60; 65; 55; 55; 60; 50; 55.Use the Lap time data for Lap .1 (see Appendix C) to test the claim that Terii finishes Lap J. on average. In less than 129 seconds. Use all twenty races given.Use the initial Public Offering’ data (see Appendix C) to test the claim that the mean offer price was $18 per share. Do not use all the data. Use your random number generator to randomly survey 15 prices.“Asian Family Reunion,” by Chau Nguyen Every two years it comes around. We all get together from different towns. In my honest opinion, It’s not a typical family reunion. Not forty, or fifty, or sixty, But how about seventy companions! The kids would play, scream, and shout One minute they’re happy, another they’ll pout. The teenagers would look, stare, and compare From how the’ look to what they wear. The men would chat about their business That they make moie, but never less. Money Is always their subject And there’s always talk of more new projects. The women get tired from all of the chats They head to the kitchen to set out the mats. Some would sit and some would stand Eating and talking with plates in their hands. Then come the games and the songs And suddenly, everyone gets along! With all that laughter, It’s sad to say That it always ends in the same old way. The’ hug and kiss and say “good-bye” And then they all begin to cty! I say that 60 percent shed their tears But my mom counted 35 people this year. She said that boys and men sjll always have their piide, So we won’t ever see them civ. I myself don’t think she’s correct, So could you please try this problem to see if you object?‘The Problem with Angels,” by Cyndy Dowling Although this problem is wholly mine, The catalyst came from the magazine, Time. On the magazine cover I did find The realm of angels tickling my mind. Inside, 69% I found to be In angels, Americans do believe. Then, ft was time to rise to the task, Ninety-five high school and college students I did ask. Viewing all as one group, Random sampling to get the scoop. So, I asked each to be true, “Do you believe in angels?” Tell me, do! Hypothesizing at the stan, Totally believing in my heart That the proportion who said yes Would be equal on this test. Lo and behold, seventy-three did arrive, Out of the sample of ninety-five. Now your job has just begun, Solve this problem and have some fun.“Blowing Bubbles,” by Sondra Prull Studying stats just made me tense, I had to find some sane defense. Some light and lifting simple play To float my math anxiety away. Blowing bubbles lifts me high Takes my troubles to the sky. POlK! They’re gone, with all my stress Bubble therapy is the best. The label said each time I blew The average number of bubbles would be at least 22. I blew and blew and this I found From 64 blows, they all are round! But the number of bubbles in 64 blows Vaiied widely, this I know. 20 per blow became the mean They deviated by 6, and not 16. From counting bubbles, I sure did relax But now I give to you your task. Was 22 a reasonable guess? Find the answer and pass this test!“Dalmatian Darnation,” by Kathy Sparling A greedy dog breeder named Spreckles Bred puppies with numerous freckles The Dalmatians he sought Possessed spot upon spot The more spots, he thought, the more shekels. His competitors did not agree That freckles would increase the fee. The’ said, “Spots are quite nice But they don’t affect price; One should breed for improved pedigree.” The breeders decided to prove This strategy was a wrong move. Breeding only for spots Would wreak havoc, they thought. His theoty they want to disprove. They proposed a contest to Spreckles Comparing dog prices to freckles. In records they looked up One hundred one pups: Dalmatians that fetched the most shekels. They asked Mr. Spreckles to name An average spot count he’d claim To bring in big bucks. Said Spreckles, “Well, shucks, It’s for one hundred one that I aim.” Said an amateur statistician Who wanted to help with this mission. “Twenty-one for the sample Standard deviation’s ample: The’ examined one hundred and one Dalmatians that fetched a good sum. They counted each spot, Mark, freckle and dot And tallied up every one. Instead of one hundred one spots They averaged ninety six dots Can they muzzle Spreckles’ Obsession with freckles Based on all the dog data they’ve got?‘MacaronI and Cheese, please! I” by Nedda Misberghl and Rachelle Hall As a poor starving student I don’t have much money to spend for even the bare necessities. So my favoite and main staple food is macaroni and cheese. ks high in taste and low In cost and nutritional value. One day, as I sat down to deterniine the meaning of life. I got a senous craving for this, oh, so important, food of my life. So I went down the sn-eel to Greatwa to get a box of macaroni and cheese, but it was SO expensive! $2.02 !!! Can you believe It? It made me stop and think. The world Is changing fast. I had thought that the mean cost of a box (the normal size, not some super-gigantIc-fam1ly-valuepack) was at most Si, but now I wasn’t so sure. However, I was determined o find out. I went to 53 of the closest gxocery stores and surveyed the prices of macaroni and cheese. Hete axe the data I wrote In my noteboolc Price per box of Mac and Cheese: • 5 stoies @ $2.02 • l5stores@S0.25 • 3stores@S1.29 • 6 stoies @ $0.35 • 4 stoies @ $2.27 • 7 soies@Sl.SO • Sstores@Sl.89 • 8 stotes @ 0.75. I could see that the cost varied but I had to sit down to figure out whether or not I was right. If it does turn out that this mouth-watering dish Is at most Si, then I’ll throw a big cheesy panv in our next statistics lab, with enough macaroni and cheese for just me. (After all, as a poor starving student I can’t be expected to feed our class of animals!)“William Shakespeare: The Tragedy of Hamlet. Prince of Denmark,” by Jacqueline Ghodsi THE CHARACTERS (in order of appearance): • HAMLET, Prince of Denmark and student of Statistics • POLONIUS, Hamlet’s tutor • HOROTIO, friend to Hamlet and fellow student Scene: The great library of the castle. In which Hamlet does his lessons Act I (The day is fair, but the face of Hamlet is clouded. He paces the large room. His tutor, Polonius, is teprimanding Hamlet regarding the latter’s recent experience. Horatio Is seated at the large table at right stage.) POLONIUS: M Lord, how cans’t thou admit that thou hast seen a ghost! It Is but a figment of your imagination! HAMLET: I beg to differ; I know of a certain! that five-and-seventy in one hundred of us, condemned to the whips and scorns of time as we are, have gazed upon a spirit of health, or goblin damn’d, be their Interns wicked or charitable. POLONIUS If thou doest Insist upon thy wretched vision then let me invest your time; be true to thy work and speak to me through the reason of the null and alternate hypotheses. (He turns to Horatio.) Did no Hamlet himself say. “What piece of work is man, how noble In reason, how Infinite in faculties? Then let no this foolishness persist. Go. Horatio, make a survey of three-and-sixty and discover what the true proportion be. For my part. I will never succumb to this fantasy, but deem man to be devoid of all reason should thy proposal of at least five-and-seventy In one hunched hold true. HORATIO (to Hamlet): What should we do. my Lord? HAMLET: Go to thy purpose. Horatio. HORATIO: To what end, my Lord? HAMLET: That you must teach me. But let me conjure you by the rights of our fellowship, by the consonance of our youth. but the obligation of our ever-preserved love, be even and direct with me, whether I am right or no. (Horatio exits, followed by Polonius, leaving Hamlet to ponder alone.) Act II (The next day. Hamlet awaits anxiously the presence of his friend, Horatio. Polonius enters and places some books upon the table just a moment before Horatio enters.) POLONIUS: So. Horatio. what Is it thou dldst reveal through thy deliberations? HORATIO: In a random survey, for which purpose thou thyself sent me forth. I did discover that one-and-forty believe fervently that the spirits of the dead walk with us. Before my God, I might not this believe, without the sensible and true avouch of mine own eyes. POLONIUS: Give thine own thoughts no tongue. Horatio. (Polonlus turns to Hamlet.) But look to’t I charge you, my Lord. Come Horatio, let us go together, for this Is not our test. (Horatio and Polonius leave together.) HAMLET: To reject, or not reject, that Is the question: whether tIs nobler In the mind to suffer the slings and anows of outrageous statistics, or to take aims against a sea of data, and, by opposing, end them. (Hamlet resignedly attends to his task.) (Curtain fal1s “Untitled.” by Stephen Chen lye often wondered how software is released and sold to the public. ironically, I work foi a company that sells products with knoisii problems. Unfortunately, most of the problems aze difficult to c,eate, which makes them difficult to fbc. I usually use the test program X, which tests the product, to ny to create a specific problem. When the test program Is run ro make an error occur, the likelihood of generating an error Is 1%. So, aimed with this knowledge, I wrote a new test program Y that will generate the same error that test program X creates, but more often. To find out If m test program Is better than the original, so that I can convince the management that [m right, I ran my test piogram to find out how often I can generate the same error. When I ran my test program 50 times, I generated the error twice. While this may not seem much better, I chink that I can convince the management to use my test program instead of the original test program. Am I right?Japanese Glrls Names’ by Kumi Furnichi It used to be vet typical for Japanese girls names to end with ‘ko.’ (The tiend might have started around my grandmothers’ generation and Its peak might have been around m mother’s generation.) “Ko” means ‘chIld” In Chinese characters. Patents would name their daughters with ko” attaching to other Chinese characters which have meanings that they want their daughters to become, such as Sachlko—happv child, Yoshlko—a good child. Yasuko—a healthy child, and so on. Howevet, I noticed recently that only two out of nine of my Japanese girlfriends at this school have names which end with “ko.” More and more, patents seem to have become cteative, modernized, and, sometimes, westernized In naming their children, I have a feeling that, whIle 70 percent or more of my mother’s generation would have names with “ko” at the end, the proportion has dropped among m peers. I wrote down all m Japanese friends’, ex-classrnates’. co-workers, and acquaintances’ names that I could remember. Following are the names. (Some are repeats.) Test to see if the proportion has dropped for this generation. Al, Akemi, Akiko, Avumi, Chiaki, Chic. Elko. En. Etiko. Fumiko, Hanimi, Hioml. Hiroko, Hiroko, Hidemi, Hisako, Hinako, izumi, Izumi, Junko, Junko, Kana, Kanako, Kanavo, Kayo, Kavoko, Kazumi. Kelko, Keiko, KeI, Kumi, Kumiko, Kvoko, Kvoko, Madoka, Maho, Mal, Malko, Maid, Mild, Mild, Mtldko, Mina, Minako, Mivako, Momoko, Nana, Naoko, Naoko, Naoko. Noriko, Rieko, Rika, Rika, Rumiko, Rd. Relko, Relko, Sachiko, Sachiko. Sachivo, Said, Savaka, Savoko, Savtui, Seiko, Shiho, Shizuka, Sumiko, Takako, Takako, Tomoe, Tomoe, Tomoko, Touko, Yasuko, Yasuko, Yasuyo, Yoko, Yoko, Yoko, Yoshiko, Yoshiko, Yoshiko, Yuka, Yukl, Vuki, Yuklko, Wiko, Vuko.‘Phillip’s Wish,” by Suzanne Osorlo My nephew likes to play Chasing the girls makes his day. He asked his mother If it is okay To get his ear pierced. She said, “No way!” To poke a hole through your ear, Is not what I want for you, dear. He argued his point quite well, Says even my macho pal, Mel, Has gotten this done. It’s all just for fun. C’mon please, mom, please, what the hell. Again Phillip complained to his mother, Saving half his friends (including their brothers) Are piercing their ears And they have no fears He wants to be like the others. She said, “I think it’s much less. We must do a hypothesis test. And If you are iight, I won’t put up a fight. But, if not, then my case will rest.” We proceeded to call fifty guys To see whose prediction would fly. Nineteen of the fifty Said piercing was nifty And earrings they’d occasionally buy. Then there’s the other thirty-one, Who said they’d never have this done. So now this poem’s finished. Will his hopes be diminished, Or will my nephew have his fun?“The Craven,” by Mark Salangsang Once upon a morning dreary In stats class I as weak and weary. Pondering over last night’s homework Whose answers were now on the board This I did and nothing more. While I nodded nearly napping Suddenly, there came a tapping. As someone gently rapping, Rapping my head as I snore. Quoth the teacher, “Sleep no more,” “In every class you fall asleep,” The teacher said, his voice was deep. “So a tally I’ve begun to keep Of every class you nap and snore. The percentage being forty-four.” “Mv deai teacher I must confess, While sleeping is what I do best. The percentage, I think, must be less, A percentage less than forty-four.” This I said and nothing more. “We’ll see,” he said and walked away, And fifty classes from that day He counted till the month of May The classes in which I napped and snored. The number he found was twenty-four. At a significance level of 0.05, Please tell me am I still alive? Or did my grade just take a dive Plunging down beneath the floor? Upon thee I hereby implore.Toastmasters Inteniational cites a repol by Gallop Poll that .10°O of Americans fear public speaking. A student believes that less than .10% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 135 report they fear public speaking. Conduct a hypothesis test to determine if the percent at her school Is less than 40%.Sixty-eight percent of online courses taught at community colleges nationwide were taught by Mi-time faculty. To test If 68°o also represents California’s percent for Mi-time faculty teaching the online classes, Long Beach City College (LBCC) In California, was randomly selected for comparison. In the same year, 3.1 of the.1.1 online courses LBCC offered were taught by MI-time faculty Conduct a hypothesis test to determine If 68% represents California. NOTE: For more accurate results, use more California community colleges and this past year’s data.According to an article In Bloomberg Businessweek, New York City’s most recent adult smoking rate Is 149b. Suppose that a survey Is conducted to deteimine this yeai’s rate. Nine out of 70 randoml chosen N.Y. City residents reply that they smoke. Conduct a hypothesis test to determine If the rate Is still 14% or If It has decreased.The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students Is older than 26.6. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Conduct a hypothesis test.Registered nurses earned an average annual salary of $69,110. For that same year. a survey was conducted of .11 California registered nurses to determine if the annual salaiy is higher than $69,110 for California nurses. The sample average was S71,121 with a sample standard deviation of S7,.89. Conduct a hypothesis test.La Leche League International reports that the mean age of weaning a child from breastfeeding is age four to five woildwide. In Amezica. most nwslng mothers wean their children much earlier. Suppose a tandom survey Is conducted of 21 U.S. mothers who recently weaned their children. The mean weaning age was nine months (3/4 year) with a standard devIation of 4 months. Conduct a hypothesis test to determine If the mean weaning age In the U.S. Is less than four years old.Over the past few decades, public health officials have examined the link between weight concerns and teen girls smoking. Researchers surveyed a group of 273 randomly selected teen girls living In Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? After conducting the test, your decision and conclusion are a. Reject H0: There Is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin. b. Do no reject H0: There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thii. c. Do not teject H0: Thete Is not sufficient evidence to conclude that more than 30°c of teen girls smoke to stay thin. d. Reject H0: There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.A statistics instnictor believes that fewer than 20% of EverWeen Valley College (EVC) students attended the opening night midnight showing of the latest Han Poaer movie. She surve s 84 of her students and finds that 11 of them attended the midnight showing. At a 1% level of significance, an appropriate conclusion is: a. Thete Is Insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Hairy Pottet Is less than 20%. b. Thete Is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Hairy Potter is mote than 20%. c. There Is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Hany Potter Is less than 200o. d. There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is at least 20%.Previously, an organization reported that teenagers spent 3.5 hours per week, on average, on the phone. The organization thinks that, cunenth; the mean is higher. Fifteen randomly chosen teenagers were asked how man how’s per week they spend on the phone. The sample mean was .1.75 hours with a sampLe standard deviation of 2.0. Conduct a hypothesis test. At a significance level of a 0.05. what Is the coned conclusion? a. There Is enough evidence to conclude that the mean number of hours is more than .175 b. There Is enough evidence to conclude that the mean number of hours is more than 4.5 c. There Is no enough evidence to conclude that the mean number of hours Is more than 4.5 d. There Is no enough evidence to conclude that the mean number of hours Is more than 4.75 Instructions: For the following ten exercises. Hypothesis testing: For the following ten exercises, answer each question. a. State the null and alternate hypothesis. b. State the p-value. C. State alpha. d. What Is your decision? e. Write a conclusion. f. Answer any other questions asked in the problem.According to the Centet for Disease Control websfte, In 2011 at least 18% of high school students have smoked a cigatene. An Introduction to Statistics class In Davies County. KY conducted a hypothesis test at the local high school (a medium slzed—appxoxlrnatelv 1,200 students—small city demographic) to determine If the local high schools percentage was lower. One hundred fifty students wete chosen at random and surveyed. Of the 150 students surveyed, 82 have smoked. Use a significance level of 005 and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.A recent survey In the N.Y. limes Almanac indicated that 4.8.8% of families own stock A broker wanted to deteimine If this survey could be valid. He surveyed a random sample of 250 families and found that 1-12 owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?Driver error can be listed as the cause of approximately 54% of all fatal auto accidents, according to the American Automobile Association. Thety randomly selected fatal accidents are examined, and ft is determined that 1.1 were caused by driver error. Using a 0.05. is the AAA proportion accurate?The US Department of Energy reported that 51.7% of homes were heated by natural gas. A random sample of 221 homes In Kentucky found that 115 were heated b natural gas. Does the evidence support the claim for Kentucky at the a = 0.05 level in Kentucky? Are the results applicable across the country? Why?For Americans using library services, the American Librar Association claims that at most 67à of patrons borrow books. The library director In Owensboro. Kentucky feels this is hot true, so she asked a local college statistic class to conduct a survey. The class iandornlv selected 100 patrons and found thar 82 borrowed books. Did the class demonsuate that the percentage was higher In C)wensboro, KY? Use a = 0.01 level of significance. What Is the possible proportion of patrons that do borrow books from the Owensboro Libra?The Weather Underground reported that the mean amount of summer rainfall for the northeastern US Is at least 11.52 inches. Ten cities In the northeast are randomly selected and the mean rainfall amount Is calculated to be 7.42 inches with a sandard deviation of 1.3 inches. At the a = 0.05 level, can It be concluded char the mean rainfall was below the reported average? What If a 0.01? Assume the amount of summer rainfall follows a normal distribution.A survey in the N.Y. limes Almanac finds the mean commute time (one way) 15 25.4 minutes for the 15 largest US cities. The Austin. TX chamber of commerce feels that Austins commute time is less and wants to publicize this fact. The mean for 25 randomly selected commuters Is 22.1 minutes with a standard deviation of 5.3 minutes. At the a 0.10 level, Is the Austin. TX commute significantly less than the mean commute time for the 15 largest US cities?A report by the Gallup Poll found that a woman visits her doctor, on average, at most 5.8 tImes each year. A random sample of 20 women results In these yearly visit totals 3; 2:1:3; 7; 2; 9;4; 6:6:8; 0:5:6:3:2:1; 3:; 1 At the a = 0.05 level can It be concluded that the sample mean Is higher than 5.8 visits per year?According to the N.Y Times Almanac the mean family size In the U.S. is 3.18. A sample of a college math class resulted In the following family sizes: 5; 4; 5; 4; 4; 3; 6; 4; 3:3:5; 5:6:3:3:2; 7; 4; 5:2:2:2:3; 2 At a = 0.05 level, Is the class mean family size greater than the national average? Does the Almanac result remain valid? Why?The student academic group on a college campus claims that freshman students study at least 2.5 hours pe day, on average. One Introduction to Statistics class was skeptical. The class took a random sample of 30 freshman students and found a mean study time of 137 minutes with a standaid deviation of 45 minutes. At a 0.01 level, Is the student academic groups claim correct?Two samples are shown in Table 10.2. Both have normal distributions. The means for the two populations are thought to be the same. Is there a difference in the means? Test at the 5% level of significance. Sample Size Sample Mean Sample Standard Deviation Population A 25 5 1 Population B 16 4.7 1.2 Table 10.2 NOTE When the sum of the sample sizes is larger than 30 ( n1+n230 ) you can use the normal distribution to approximate the Student's t.A study is done to determine if Company A retains its workers longer than Company B. Company A samples 15workers, and their average time with the company is five years with a standard deviation of 1.2. Company B samples 20 workers, and their average time with the company is 4.5 years with a standard deviation of 0.8. The populations are normally distributed. a. Are the population standard deviations known? b. Conduct an appropriate hypothesis test. At the 5% significance level, what is your conclusion?Weighted alpha is a measure of risk-adjusted performance of stocks over a period of a year. A high positive weighted alpha signifies a stock whose price has risen while a small positive weighted alpha indicates an unchanged stock price during the time period. Weighted alpha is used to identify companies with strong upward or downward trends. The weighted alpha for the top 30 stocks of banks in the northeast and in the west as identified by Nasdaq on May 24, 2013 are listed in Table 10.6 and Table 10.7, respectively. 94.2 75.2 69.6 52.0 48.0 41.9 36.4 33.4 31.5 27.6 77.3 71.9 67.5 50.6 46.2 38.4 35.2 33.0 28.7 26.5 76.3 71.7 56.3 48.7 43.2 37.6 33.7 31.8 28.5 26.0 Table 10.6 Northeast 126 70.6 65.2 51.4 45.5 37.0 33.0 29.6 23.7 22.6 116.1 70.6 58.2 51.2 43.2 36.0 31.4 28.7 23.5 21.6 78.2 68.2 55.6 50.3 39.0 34.1 31.0 25.3 23.4 21.5 Table 10.7 West Is there a difference in the weighted alpha of the top 30 stocks of banks in the northeast and in the west? Test at a 5% significance level. Answer the following questions: a. Is this a test of two means or two proportions? b. Are the population standard deviations known or unknown? c. Which distribution do you use to perform the test? d. What is the random variable? e. What are the null and alternative hypotheses? Write the null and alternative hypotheses in words and in symbols. f. Is this test right, left, or two tailed? g. What is the p-value? h. Do you reject or not reject the null hypothesis? i. At the ___ level of significance, from the sample data, there ______ (is/is not) sufficient evidence to conclude that ______. j. Calculate Cohen’s d and interpret it.The means of the number of revolutions per minute of two competing engines are to be compared. Thirty engines are randomly assigned to be tested. Both populations have normal distributions. Table 10.9 shows the result. Do the data indicate that Engine 2 has higher RPM than Engine 1? Test at a 5% level of significance. Engine Sample Mean Number of RPM Population Standard Deviation 1 1500 50 2 1600 60 Table 10.9 Two types of valves are being tested to determine if there is a difference in pressure tolerances. Fifteen out ofa random sample of 100 of Valve A cracked under 4,500 psi. Six out of a random sample of 100 of Valve B cracked under 4,500 psi. Test at a 5% level of significance.A concerned group of citizens wanted to know if the proportion of forcible rapes in Texas was different in 2011 than in 2010. Their research showed that of the 113,231 violent crimes in Texas in 2010, 7,622 of them were forcible rapes. In 2011, 7,439 of the 104,873 violent crimes were in the forcible rape category. Test at a 5% significance level. Answer the following questions: a. Is this a test of two means or two proportions? b. Which distribution do you use to perform the test? c. What is the random variable? d. What are the null and alternative hypothesis? Write the null and alternative hypothesis in symbols. e. Is this test right-, left-, or two-tailed? f. What is the p-value? g. Do you reject or not reject the null hypothesis? h. At the ___ level of significance, from the sample data, there ______ (is/is not) sufficient evidence to conclude that____________.A study was conducted to investigate how effective a new diet was in lowering cholesterol. Results for the randomly selected subjects are shown in the table. The differences have a normal distribution. Are the subjects’ cholesterol levels lower on average after the diet? Test at the 5% level. Subject A B C D E F G H I Before 209 210 205 198 216 217 238 240 222 After 199 207 189 209 217 202 211 223 201 A new prep class was designed to improve SAT test scores. Five students were selected at random. Their scores on two practice exams were recorded, one before the class and one after. The data recorded in Table 10.15. Are the scores, on average, higher after the class? Test at a 5% level. SAT Scores Student 1 Student 2 Student 3 Student 4 Score before class 1840 1960 1920 2150 Score after class 1920 2160 2200 2100 Table 10.15 Five ball players think they can throw the same distance with their dominant hand (throwing) and off-hand (catching hand). The data were collected and recorded in Table 10.17. Conduct a hypothesis test to determine whether the mean difference in distances between the dominant and off-hand is significant. Test at the 5% level. Player 1 Player 2 Player 3 Player 4 Player 5 Dominant Hand 120 111 135 140 125 Off-hand 105 109 98 111 99 Table 10.17 Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion It is believed that 70% of males pass their drivers test in the first attempt, while 65% of females pass the test in the first attempt. Of interest is whether the proportions are in fact equal.Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion A new laundry detergent is tested on consumers. Of interest is the proportion of consumers who prefer the new brand over the leading competitor. A study is done to test this.Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without the new treatment. The same windshields are then treated, and the experiment is run again. A hypothesis test is conducted.Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion The known standard deviation in salary for all mid-level professionals in the financial industry is $11,000. Company A and Company B are in the financial industry. Suppose samples are taken of mid-level professionals from Company A and from Company B. The sample mean salary for mid-level professionals in Company A is $80,000. The sample mean salary for mid-level professionals in Company B is $96,000. Company A and Company B management want to know if their midlevel professionals are paid differently, on average.Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion The average worker in Germany gets eight weeks of paid vacation.Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion According to a television commercial, 80% of dentists agree that Ultrafresh toothpaste is the best on the market Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion It is believed that the average grade on an English essay in a particular school system for females is higher than for males. A random sample of 31 females had a mean score of 82 with a standard deviation of three, and a random sample of 25 males had a mean score of 76 with a standard deviation of four.Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion The league mean batting average is 0.280 with a known standard deviation of 0.06. The Rattlers and the Vikings belong to the league. The mean batting average for a sample of eight Rattlers is 0.210, and the mean batting average for a sample of eight Vikings is 0.260. There are 24 players on the Rattlers and 19 players on the Vikings. Are the batting averages of the Rattlers and Vikings statistically different?Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion In a random sample of 100 forests in the United States, 56 were coniferous or contained conifers. In a random sample of 80 forests in Mexico, 40 were coniferous or contained conifers. Is the proportion of conifers in the United States statistically more than the proportion of conifers in Mexico?Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion A new medicine is said to help improve sleep. Eight subjects are picked at random and given the medicine. The means hours slept for each person were recorded before starting the medication and after.Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion It is thought that teenagers sleep more than adults on average. A study is done to verify this. A sample of 16 teenagers has a mean of 8.9 hours slept and a standard deviation of 1.2. A sample of 12 adults has a mean of 6.9 hours slept and a standard deviation of 0.6.Two Population Means with Unknown Standard Deviations Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for independent group means, population standard deviations, and/or variances known independent group means, population standard deviations, and/or variances unknown matched or paired samples single mean two proportions single proportion Varsity athletes practice five times a week, on average.

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