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All Textbook Solutions for Introductory Statistics
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 sample of 12 in-state graduate school programs at school A has a mean tuition of $64,000 with a standard deviation of $8,000. At school B, a sample of 16 in-state graduate programs has a mean of $80,000 with a standard deviation of $6,000.On average, are the mean tuitions 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 A new WiFi range booster is being offered to consumers. A researcher tests the native range of 12 different routers under the same conditions. The ranges are recorded. Then the researcher uses the new WiFi range booster and records the new ranges. Does the new WiFi range booster do a better job?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 high school principal claims that 30% of student athletes drive themselves to school, while 4% of non-athletes drive themselves to school. In a sample of 20 student athletes, 45% drive themselves to school. In a sample of 35 non-athlete students, 6% drive themselves to school. Is the percent of student athletes who drive themselves to school more than the percent of nonathletes?Use the following information to answer the next three exercises: A study is done to determine which of two soft drinks has more sugar. There are 13 cans of Beverage A in a sample and six cans of Beverage B. The mean amount of sugar in Beverage A is 36 grams with a standard deviation of 0.6 grams. The mean amount of sugar in Beverage B is 38 grams with a standard deviation of 0.8 grams. The researchers believe that Beverage B has more sugar than Beverage A, on average. Both populations have normal distributions. Are standard deviations known or unknown?Use the following information to answer the next three exercises: A study is done to determine which of two soft drinks has more sugar. There are 13 cans of Beverage A in a sample and six cans of Beverage B. The mean amount of sugar in Beverage A is 36 grams with a standard deviation of 0.6 grams. The mean amount of sugar in Beverage B is 38 grams with a standard deviation of 0.8 grams. The researchers believe that Beverage B has more sugar than Beverage A, on average. Both populations have normal distributions. What is the random variable?Use the following information to answer the next three exercises: A study is done to determine which of two soft drinks has more sugar. There are 13 cans of Beverage A in a sample and six cans of Beverage B. The mean amount of sugar in Beverage A is 36 grams with a standard deviation of 0.6 grams. The mean amount of sugar in Beverage B is 38 grams with a standard deviation of 0.8 grams. The researchers believe that Beverage B has more sugar than Beverage A, on average. Both populations have normal distributions. Is this a one-tailed or two-tailed test?Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. Is this a test of means or proportions?Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. State the null and alternative hypotheses. a. H0: __________ b. Ha: __________Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. Is this a right-tailed, left-tailed, or two-tailed test?Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. In symbols, what is the random variable of interest for this test?Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. In words, define the random variable of interest for this test.Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. Which distribution (normal or Student's t) would you use for this hypothesis test?Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. Explain why you chose the distribution you did for Exercise 10.24.Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. Calculate the test statistic and p-value.Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. Sketch a graph of the situation. Label the horizontal axis. Mark the hypothesized difference and the sample difference. Shade the area corresponding to the p-value.Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. Find the p-value.Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. At a pre-conceived a = 0.05, what is your: a. Decision: b. Reason for the decision: c. Conclusion (write out in a complete sentence):Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites. Does it appear that the means are the same? Why or why not?Two Population Means with Known Standard Deviations Use the following information to answer the next five exercises. The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. Table 10.18 shows the result. Scouters believe that Rodriguez pitches a speedier fastball. Pitcher Sample Mean Speed of Pitches (mph) Population Standard Deviation Wesley 86 3 Rodriguez 91 7 Table 10.18 What is the random variable?Two Population Means with Known Standard Deviations. Use the following information to answer the next five exercises. The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. Table 10.18 shows the result. Scouters believe that Rodriguez pitches a speedier fastball. Pitcher Sample Mean Speed of Pitches (mph) Population Standard Deviation Wesley 86 3 Rodriguez 91 7 Table 10.18 State the null and alternative hypotheses.Two Population Means with Known Standard Deviations Use the following information to answer the next five exercises. The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. Table 10.18 shows the result. Scouters believe that Rodriguez pitches a speedier fastball. Pitcher Sample Mean Speed of Pitches (mph) Population Standard Deviation Wesley 86 3 Rodriguez 91 7 Table 10.18 What is the test statistic?Two Population Means with Known Standard Deviations. Use the following information to answer the next five exercises. The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. Table 10.18 shows the result. Scouters believe that Rodriguez pitches a speedier fastball. Pitcher Sample Mean Speed of Pitches (mph) Population Standard Deviation Wesley 86 3 Rodriguez 91 7 Table 10.18 What is the p-value?Two Population Means with Known Standard Deviations Use the following information to answer the next five exercises. The mean speeds of fastball pitches from two different baseball pitchers are to be compared. A sample of 14 fastball pitches is measured from each pitcher. The populations have normal distributions. Table 10.18 shows the result. Scouters believe that Rodriguez pitches a speedier fastball. Pitcher Sample Mean Speed of Pitches (mph) Population Standard Deviation Wesley 86 3 Rodriguez 91 7 Table 10.18 At the 1% significance level, what is your conclusion?Use the following information to answer the next five exercises. A researcher is testing the effects of plant food on plant growth. Nine plants have been given the plant food. Another nine plants have not been given the plant food. The heights of the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller. Plant Group Sample Mean Height of Plants (inches) Population Standard Deviation Food 16 2.5 No food 14 1.5 Table 10.19 Is the population standard deviation known or unknown?Use the following information to answer the next five exercises. A researcher is testing the effects of plant food on plant growth. Nine plants have been given the plant food. Another nine plants have not been given the plant food. The heights of the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller. Plant Group Sample Mean Height of Plants (inches) Population Standard Deviation Food 16 2.5 No food 14 1.5 Table 10.19 State the null and alternative hypotheses.Use the following information to answer the next five exercises. A researcher is testing the effects of plant food on plant growth. Nine plants have been given the plant food. Another nine plants have not been given the plant food. The heights of the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller. Plant Group Sample Mean Height of Plants (inches) Population Standard Deviation Food 16 2.5 No food 14 1.5 Table 10.19 What is the p-value?Use the following information to answer the next five exercises. A researcher is testing the effects of plant food on plant growth. Nine plants have been given the plant food. Another nine plants have not been given the plant food. The heights of the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller. Plant Group Sample Mean Height of Plants (inches) Population Standard Deviation Food 16 2.5 No food 14 1.5 Table 10.19 Draw the graph of the p-value.Use the following information to answer the next five exercises. A researcher is testing the effects of plant food on plant growth. Nine plants have been given the plant food. Another nine plants have not been given the plant food. The heights of the plants are recorded after eight weeks. The populations have normal distributions. The following table is the result. The researcher thinks the food makes the plants grow taller. Plant Group Sample Mean Height of Plants (inches) Population Standard Deviation Food 16 2.5 No food 14 1.5 Table 10.19 At the 1% significance level, what is your conclusion?Use the following information to answer the next five exercises. Two metal alloys are being considered as material for ball bearings. The mean melting point of the two alloys is to be compared. 15 pieces of each metal are being tested. Both populations have normal distributions. The following table is the result. It is believed that Alloy Zeta has a different melting point. Sample Mean Melting Temperatures (°F) Population Standard Deviation Alloy Gamma 800 95 Alloy Zeta 900 105 Table 10.20 State the null and alternative hypotheses.Use the following information to answer the next five exercises. Two metal alloys are being considered as material for ball bearings. The mean melting point of the two alloys is to be compared. 15 pieces of each metal are being tested. Both populations have normal distributions. The following table is the result. It is believed that Alloy Zeta has a different melting point. Sample Mean Melting Temperatures (°F) Population Standard Deviation Alloy Gamma 800 95 Alloy Zeta 900 105 Table 10.20 Is this a right-, left-, or two-tailed test?Use the following information to answer the next five exercises. Two metal alloys are being considered as material for ball bearings. The mean melting point of the two alloys is to be compared. 15 pieces of each metal are being tested. Both populations have normal distributions. The following table is the result. It is believed that Alloy Zeta has a different melting point. Sample Mean Melting Temperatures (°F) Population Standard Deviation Alloy Gamma 800 95 Alloy Zeta 900 105 Table 10.20 What is the p-value?Use the following information to answer the next five exercises. Two metal alloys are being considered as material for ball bearings. The mean melting point of the two alloys is to be compared. 15 pieces of each metal are being tested. Both populations have normal distributions. The following table is the result. It is believed that Alloy Zeta has a different melting point. Sample Mean Melting Temperatures (°F) Population Standard Deviation Alloy Gamma 800 95 Alloy Zeta 900 105 Table 10.20 Draw the graph of the p-value.Use the following information to answer the next five exercises. Two metal alloys are being considered as material for ball bearings. The mean melting point of the two alloys is to be compared. 15 pieces of each metal are being tested. Both populations have normal distributions. The following table is the result. It is believed that Alloy Zeta has a different melting point. Sample Mean Melting Temperatures (°F) Population Standard Deviation Alloy Gamma 800 95 Alloy Zeta 900 105 Table 10.20 At the 1% significance level, what is your conclusion?Comparing Two Independent Population Proportions. Use the following information for the next five exercises. Two types of phone operating system are being tested to determine if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with OS1 had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with OS2 had system failures within the first eight hours of operation. OS2 is believed to be more stable (have fewer crashes) than OS1. Is this a test of means or proportions?Comparing Two Independent Population Proportions. Use the following information for the next five exercises. Two types of phone operating system are being tested to determine if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with OS1 had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with OS2 had system failures within the first eight hours of operation. OS2 is believed to be more stable (have fewer crashes) than OS1. What is the random variable?Comparing Two Independent Population Proportions. Use the following information for the next five exercises. Two types of phone operating system are being tested to determine if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with OS1 had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with OS2 had system failures within the first eight hours of operation. OS2 is believed to be more stable (have fewer crashes) than OS1. State the null and alternative hypothesesComparing Two Independent Population Proportions. Use the following information for the next five exercises. Two types of phone operating system are being tested to determine if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with OS1 had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with OS2 had system failures within the first eight hours of operation. OS2 is believed to be more stable (have fewer crashes) than OS1. What is the p-value?Comparing Two Independent Population Proportions. Use the following information for the next five exercises. Two types of phone operating system are being tested to determine if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with OS1 had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with OS2 had system failures within the first eight hours of operation. OS2 is believed to be more stable (have fewer crashes) than OS1. What can you conclude about the two operating systems?Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. Is this a test of means or proportions?Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. State the null and alternative hypotheses. a. H0: _________ b. Ha: _________Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. Is this a right-tailed, left-tailed, or two-tailed test? How do you know?Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. What is the random variable of interest for this test?Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. In words, define the random variable for this test.Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. Which distribution (normal or Student's t) would you use for this hypothesis test?Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. Explain why you chose the distribution you did for the Exercise 10.56.Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. Calculate the test statistic.Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. Sketch a graph of the situation. Mark the hypothesized difference and the sample difference. Shade the area corresponding to the p-value. Figure 10.17Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. Find the p-value.Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. At a pre-conceived a = 0.05, what is your: a. Decision: b. Reason for the decision: c. Conclusion (write out in a complete sentence):Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota. Does it appear that the proportion of Nevadans who are two or more races is higher than the proportion of North Dakotans? Why or why not?Matched or Paired Samples Use the following information to answer the next five exercises. A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in Table 10.21. The “before” value is matched to an “after” value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level. Installation A B C D E F G H Before 3 6 4 2 5 8 2 6 After 1 5 2 0 1 0 2 2 Table 10.21 What is the random variable?Matched or Paired Samples Use the following information to answer the next five exercises. A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in Table 10.21. The “before” value is matched to an “after” value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level. Installation A B C D E F G H Before 3 6 4 2 5 8 2 6 After 1 5 2 0 1 0 2 2 Table 10.21 State the null and alternative hypotheses.Matched or Paired Samples Use the following information to answer the next five exercises. A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in Table 10.21. The “before” value is matched to an “after” value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level. Installation A B C D E F G H Before 3 6 4 2 5 8 2 6 After 1 5 2 0 1 0 2 2 Table 10.21 What is the p-value?Matched or Paired Samples Use the following information to answer the next five exercises. A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in Table 10.21. The “before” value is matched to an “after” value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level. Installation A B C D E F G H Before 3 6 4 2 5 8 2 6 After 1 5 2 0 1 0 2 2 Table 10.21 Draw the graph of the p-value.Matched or Paired Samples Use the following information to answer the next five exercises. A study was conducted to test the effectiveness of a software patch in reducing system failures over a six-month period. Results for randomly selected installations are shown in Table 10.21. The “before” value is matched to an “after” value, and the differences are calculated. The differences have a normal distribution. Test at the 1% significance level. Installation A B C D E F G H Before 3 6 4 2 5 8 2 6 After 1 5 2 0 1 0 2 2 Table 10.21 What conclusion can you draw about the software patch?Use the following information to answer next five exercises. A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the 1% significance level. Subject A B C D E F Before 3 4 3 2 4 5 After 4 5 6 4 5 7 Table 10.23 State the null and alternative hypotheses.Use the following information to answer next five exercises. A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the 1% significance level. Subject A B C D E F Before 3 4 3 2 4 5 After 4 5 6 4 5 7 Table 10.23 What is the p-value?Use the following information to answer next five exercises. A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the 1% significance level. Subject A B C D E F Before 3 4 3 2 4 5 After 4 5 6 4 5 7 Table 10.23 What is the sample mean difference?Use the following information to answer next five exercises. A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the 1% significance level. Subject A B C D E F Before 3 4 3 2 4 5 After 4 5 6 4 5 7 Table 10.23 Draw the graph of the p-value.Use the following information to answer next five exercises. A study was conducted to test the effectiveness of a juggling class. Before the class started, six subjects juggled as many balls as they could at once. After the class, the same six subjects juggled as many balls as they could. The differences in the number of balls are calculated. The differences have a normal distribution. Test at the 1% significance level. Subject A B C D E F Before 3 4 3 2 4 5 After 4 5 6 4 5 7 Table 10.23 What conclusion can you draw about the juggling class?Use the following information to answer the next five exercises. A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level. Patient A B C D E F Before 161 162 165 162 166 171 After 158 159 166 160 167 169 Table 10.23 State the null and alternative hypothesesUse the following information to answer the next five exercises. A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level. Patient A B C D E F Before 161 162 165 162 166 171 After 158 159 166 160 167 169 Table 10.23 What is the test statistic?Use the following information to answer the next five exercises. A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level. Patient A B C D E F Before 161 162 165 162 166 171 After 158 159 166 160 167 169 Table 10.23 What is the p-value?Use the following information to answer the next five exercises. A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level. Patient A B C D E F Before 161 162 165 162 166 171 After 158 159 166 160 167 169 Table 10.23 What is the sample mean difference?Use the following information to answer the next five exercises. A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level. Patient A B C D E F Before 161 162 165 162 166 171 After 158 159 166 160 167 169 Table 10.23 What is the conclusion?The mean number of English courses taken in a twoyear time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from 29 males and 16 females. The males took an average of three English courses with a standard deviation of 0.8. The females took an average of four English courses with a standard deviation of 1.0. Are the means statistically the same?A student at a four-year college claims that mean enrollment at fouryear colleges is higher than at twoyear colleges in the United States. Two surveys are conducted. Of the 35 twoyear colleges surveyed, the mean enrollment was 5,068 with a standard deviation of 4,777. Of the 35 four-year colleges surveyed, the mean enrollment was 5,466 with a standard deviation of 8,191.At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis. Relaxed time (seconds) Jumping time (seconds) 26 21 47 40 30 28 22 21 23 25 45 43 37 35 29 32 Table 10.24Mean entry-level salaries for college graduates with mechanical engineering degrees and electrical engineering degrees are believed to be approximately the same. A recruiting office thinks that the mean mechanical engineering salary is actually lower than the mean electrical engineering salary. The recruiting office randomly surveys 50 entry level mechanical engineers and 60 entry level electrical engineers. Their mean salaries were $46,100 and $46,700, respectively. Their standard deviations were $3,450 and $4,210, respectively. Conduct a hypothesis test to determine if you agree that the mean entry-level mechanical engineering salary is lower than the mean entry-level electrical engineering salary.Marketing companies have collected data implying that teenage girls use more ring tones on their cellular phones than teenage boys do. In one particular study of 40 randomly chosen teenage girls and boys (20 of each) with cellular phones, the mean number of ring tones for the girls was 3.2 with a standard deviation of 1.5. The mean for the boys was 1.7 with a standard deviation of 0.8. Conduct a hypothesis test to determine if the means are approximately the same or if the girls’ mean is higher than the boys’ mean.Use the information from Appendix C to answer the next four exercises. Using the data from Lap 1 only, conduct a hypothesis test to determine if the mean time for completing a lap in races is the same as it is in practices.Use the information from Appendix C to answer the next four exercises. Repeat the test in Exercise 10.83, but use Lap 5 data this time.Use the information from Appendix C to answer the next four exercises. Repeat the test in Exercise 10.83, but this time combine the data from Laps 1 and 5.Use the information from Appendix C to answer the next four exercises. In two to three complete sentences, explain in detail how you might use Terri Vogel’s data to answer the following question. “Does Terri Vogel drive faster in races than she does in practices?”Use the following information to answer the next two exercises. The Eastern and Western Major League Soccer conferences have a new Reserve Division that allows new players to develop their skills. Data for a randomly picked date showed the following annual goals Western Eastern Los Angeles 9 D.C. United 9 FC Dallas 3 Chicago 8 Chivas USA 4 Columbus 7 Real Salt Lake 3 New England 6 Colorado 4 MetroStars 5 San Jose 4 Kansas City 3 Table 10.25 Conduct a hypothesis test to answer the next two exercises. The exact distribution for the hypothesis test is: a. the normal distribution b. the Student's t-distribution c. the uniform distribution d. the exponential distributionUse the following information to answer the next two exercises. The Eastern and Western Major League Soccer conferences have a new Reserve Division that allows new players to develop their skills. Data for a randomly picked date showed the following annual goals Western Eastern Los Angeles 9 D.C. United 9 FC Dallas 3 Chicago 8 Chivas USA 4 Columbus 7 Real Salt Lake 3 New England 6 Colorado 4 MetroStars 5 San Jose 4 Kansas City 3 Table 10.25 Conduct a hypothesis test to answer the next two exercises. If the level of significance is 0.05, the conclusion is: a. There is sufficient evidence to conclude that the W Division teams score fewer goals, on average, than the E teams b. There is insufficient evidence to conclude that the W Division teams score more goals, on average, than the E teams. c. There is insufficient evidence to conclude that theWteams score fewer goals, on average, than the E teams score. d. Unable to determineSuppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. She takes random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91. The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. The “day” subscript refers to the statistics day students. The “night” subscript refers to the statistics night students. A concluding statement is: a. There is sufficient evidence to conclude that statistics night students' mean on Exam 2 is better than the statistics day students' mean on Exam 2. b. There is insufficient evidence to conclude that the statistics day students' mean on Exam 2 is better than the statistics night students' mean on Exam 2. c. There is insufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2. d. There is sufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2.Researchers interviewed street prostitutes in Canada and the United States. The mean age of the 100 Canadian prostitutes upon entering prostitution was 18 with a standard deviation of six. The mean age of the 130 United States prostitutes upon entering prostitution was 20 with a standard deviation of eight. Is the mean age of entering prostitution in Canada lower than the mean age in the United States? Test at a 1% significance level.A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds.Suppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. She takes random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91, respectively. The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. The “day” subscript refers to the statistics day students. The“night” subscript refers to the statistics night students. An appropriate alternative hypothesis for the hypothesis test is: a. daynight b. daynight c. day=night d. daynightA study is done to determine if students in the California state university system take longer to graduate, on average, than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are 1.5811 years and 1 year, respectively. The following data are collected. The California state university system students took on average 4.5 years with a standard deviation of 0.8. The private university students took on average 4.1 years with a standard deviation of 0.3.Parents of teenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was $679. For 23 teenage girls, it was $559. From past years, it is known that the population standard deviation for each group is $180. Determine whether or not you believe that the mean cost for auto insurance for teenage boys is greater than that for teenage girls.A group of transfer bound students wondered if they will spend the same mean amount on texts and supplies each year at their four-year university as they have at their community college. They conducted a random survey of 54 students at their community college and 66 students at their local four-year university. The sample means were $947 and $1,011, respectively. The population standard deviations are known to be $254 and $87, respectively. Conduct a hypothesis test to determine if the means are statistically the same.Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 31 mpg with a standard deviation of seven mpg. Thirty-one non-hybrid sedans get a mean of 22 mpg with a standard deviation of four mpg. Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test to evaluate the manufacturers claim.A baseball fan wanted to know if there is a difference between the number of games played in a World Series when the American League won the series versus when the National League won the series. From 1922 to 2012, the population standard deviation of games won by the American League was 1.14, and the population standard deviation of games won by the National League was 1.11. Of 19 randomly selected World Series games won by the American League, the mean number of games won was 5.76. The mean number of 17 randomly selected games won by the National League was 5.42. Conduct a hypothesis test.One of the questions in a study of marital satisfaction of dual-career couples was to rate the statement “I’m pleased with the way we divide the responsibilities for childcare.” The ratings went from one (strongly agree) to five (strongly disagree). Table 10.26 contains ten of the paired responses for husbands and wives. Conduct a hypothesis test to see if the mean difference in the husband’s versus the wife’s satisfaction level is negative (meaning that, within the partnership, the husband is happier than the wife). Wife’s Score 2 2 3 3 4 2 1 1 2 4 Husband’s Score 2 2 1 3 2 1 1 1 2 4 Table 10.26A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them..We are interested in whether the proportions of female suicide victims for ages 15 to 24 are the same for the whites and the blacks races in the United States. We randomly pick one year, 1992, to compare the races. The number of suicides estimated in the United States in 1992 for white females is 4,930. Five hundred eighty were aged 15 to 24. The estimate for black females is 330. Forty were aged 15 to 24. We will let female suicide victims be our populationElizabeth Mjelde, an art history professor, was interested in whether the value from the Golden Ratio formula, (larger+smallerdimentionlargerdimention) was the same in the Whitney Exhibit for works from 1900 to 1919 as for works from 1920 to 1942. Thirty-seven early works were sampled, averaging 1.74 with a standard deviation of 0.11. Sixty-five of the later works were sampled, averaging 1.746 with a standard deviation of 0.1064. Do you think that there is a significant difference in the Golden Ratio calculation?A recent year was randomly picked from 1985 to the present. In that year, there were 2,051 Hispanic students at Cabrillo College out of a total of 12,328 students. At Lake Tahoe College, there were 321 Hispanic students out of a total of 2,441 students. In general, do you think that the percent of Hispanic students at the two colleges is basically the same or different?Use the following information to answer the next three exercises. Neuroinvasive West Nile virus is a severe disease that affects a person’s nervous system . It is spread by the Culex species of mosquito. In the United States in 2010 there were 629 reported cases of neuroinvasive West Nile virus out of a total of 1,021 reported cases and there were 486 neuroinvasive reported cases out of a total of 712 cases reported in 2011. Is the 2011 proportion of neuroinvasive West Nile virus cases more than the 2010 proportion of neuroinvasive West Nile virus cases? Using a 1% level of significance, conduct an appropriate hypothesis test. • “2011” subscript: 2011 group. • “2010” subscript: 2010 group This is: a. a test of two proportions b. a test of two independent means c. a test of a single mean d. a test of matched pairs.Use the following information to answer the next three exercises. Neuroinvasive West Nile virus is a severe disease that affects a person’s nervous system . It is spread by the Culex species of mosquito. In the United States in 2010 there were 629 reported cases of neuroinvasive West Nile virus out of a total of 1,021 reported cases and there were 486 neuroinvasive reported cases out of a total of 712 cases reported in 2011. Is the 2011 proportion of neuroinvasive West Nile virus cases more than the 2010 proportion of neuroinvasive West Nile virus cases? Using a 1% level of significance, conduct an appropriate hypothesis test. • “2011” subscript: 2011 group. • “2010” subscript: 2010 group\ An appropriate null hypothesis is: a. p2011p2010 b. p2011p2010 c. p2011p2010 d. p2011p2010Use the following information to answer the next three exercises. Neuroinvasive West Nile virus is a severe disease that affects a person’s nervous system . It is spread by the Culex species of mosquito. In the United States in 2010 there were 629 reported cases of neuroinvasive West Nile virus out of a total of 1,021 reported cases and there were 486 neuroinvasive reported cases out of a total of 712 cases reported in 2011. Is the 2011 proportion of neuroinvasive West Nile virus cases more than the 2010 proportion of neuroinvasive West Nile virus cases? Using a 1% level of significance, conduct an appropriate hypothesis test. • “2011” subscript: 2011 group. • “2010” subscript: 2010 group\ The p-value is 0.0022. At a 1% level of significance, the appropriate conclusion is a. There is sufficient evidence to conclude that the proportion of people in the United States in 2011 who contracted neuroinvasive West Nile disease is less than the proportion of people in the United States in 2010 who contracted neuroinvasive West Nile disease. b. There is insufficient evidence to conclude that the proportion of people in the United States in 2011 who contracted neuroinvasive West Nile disease is more than the proportion of people in the United States in 2010 who contracted neuroinvasive West Nile disease. c. There is insufficient evidence to conclude that the proportion of people in the United States in 2011 who contracted neuroinvasive West Nile disease is less than the proportion of people in the United States in 2010 who contracted neuroinvasive West Nile disease. d. There is sufficient evidence to conclude that the proportion of people in the United States in 2011 who contracted neuroinvasiveWest Nile disease is more than the proportion of people in the United States in 2010 who contracted neuroinvasive West Nile disease.Researchers conducted a study to find out if there is a difference in the use of eReaders by different age groups. Randomly selected participants were divided into two age groups. In the 16- to 29-year-old group, 7% of the 628 surveyed use eReaders, while 11% of the 2,309 participants 30 years old and older use eReaders.Adults aged 18 years old and older were randomly selected for a survey on obesity. Adults are considered obese if their body mass index (BMI) is at least 30. The researchers wanted to determine if the proportion of women who are obese in the south is less than the proportion of southern men who are obese. The results are shown in Table 10.27. Test at the 1% level of significance. Number who are obese Sample size Men 42,769 155,525 Women 67,169 248,775 Table 10.27Two computer users were discussing tablet computers. A higher proportion of people ages 16 to 29 use tablets than the proportion of people age 30 and older. Table 10.28 details the number of tablet owners for each age group. Test at the 1% level of significance. 1629 year olds 30 years old and older Own a Tablet 69 231 Sample Size 628 2,309 Table 10.28A group of friends debated whether more men use smartphones than women. They consulted a research study of smartphone use among adults. The results of the survey indicate that of the 973 men randomly sampled, 379 use smartphones. For women, 404 of the 1,304 who were randomly sampled use smartphones. Test at the 5% level of significance.While her husband spent 21/2. hours picking out new speakers, a statistician decided to determine whether the percent of men who enjoy shopping for electronic equipment is higher than the percent of women who enjoy shopping for electronic equipment. The population was Saturday afternoon shoppers. Out of 67 men, 24 said they enjoyed the activity. Eight of the 24 women surveyed claimed to enjoy the activity. Interpret the results of the survey.We are interested in whether children’s educational computer software costs less, on average, than children’s entertainment software. Thirty-six educational software titles were randomly picked from a catalog. The mean cost was $31.14 with a standard deviation of $4.69. Thirty-five entertainment software titles were randomly picked from the same catalog. The mean cost was $33.86 with a standard deviation of $10.87. Decide whether children’s educational software costs less, on average, than children’s entertainment software.Joan Nguyen recently claimed that the proportion of college-age males with at least one pierced ear is as high as the proportion of college-age females. She conducted a survey in her classes. Out of 107 males, 20 had at least one pierced ear. Out of 92 females, 47 had at least one pierced ear. Do you believe that the proportion of males has reached the proportion of females?Use the data sets found in Appendix C to answer this exercise. Is the proportion of race laps Terri completes slower than 130 seconds less than the proportion of practice laps she completes slower than 135 seconds?"To Breakfast or Not to Breakfast?" by Richard Ayore In the American society, birthdays are one of those days that everyone looks forward to. People of different ages and peer groups gather to mark the 18th, 20th, …, birthdays. During this time, one looks back to see what he or she has achieved for the past year and also focuses ahead for more to come. If, by any chance, I am invited to one of these parties, my experience is always different. Instead of dancing around with my friends while the music is booming, I get carried away by memories of my family back home in Kenya. I remember the good times I had with my brothers and sister while we did our daily routine. Every morning, I remember we went to the shamba (garden) to weed our crops. I remember one day arguing with my brother as to why he always remained behind just to join us an hour later. In his defense, he said that he preferred waiting for breakfast before he came to weed. He said, “This is why I always work more hours than you guys!” And so, to prove him wrong or right, we decided to give it a try. One day we went to work as usual without breakfast, and recorded the time we could work before getting tired and stopping. On the next day, we all ate breakfast before going to work. We recorded how long we worked again before getting tired and stopping. Of interest was our mean increase in work time. Though not sure, my brother insisted that it was more than two hours. Using the data in Table 10.29, solve our problem. Work hours with breakfast Work hours without breakfast 8 6 7 5 9 5 5 4 9 7 8 7 10 7 7 5 6 6 9 5 Table 10.29Ten individuals went on a lowfat diet for 12 weeks to lower their cholesterol. The data are recorded in Table 10.30. Do you think that their cholesterol levels were significantly lowered? Starting cholesterol level Ending cholesterol level 140 140 220 230 110 120 240 220 200 190 180 150 190 200 360 300 280 300 260 240 Table 10.30Use the following information to answer the next two exercises. A new AIDS prevention drug was tried on a group of 224 HIV positive patients. Forty-five patients developed AIDS after four years. In a control group of 224 HIV positive patients, 68 developed AIDS after four years. We want to test whether the method of treatment reduces the proportion of patients that develop AIDS after four years or if the proportions of the treated group and the untreated group stay the same. Let the subscript t = treated patient and ut = untreated patient. The appropriate hypotheses are: a. H0:ptputandHa:ptput b. H0:ptputandHa:ptput c. H0:pt=putandHa:ptput d. H0:pt=putandHa:ptputUse the following information to answer the next two exercises. A new AIDS prevention drug was tried on a group of 224 HIV positive patients. Forty-five patients developed AIDS after four years. In a control group of 224 HIV positive patients, 68 developed AIDS after four years. We want to test whether the method of treatment reduces the proportion of patients that develop AIDS after four years or if the proportions of the treated group and the untreated group stay the same. Let the subscript t = treated patient and ut = untreated patient. If the p-value is 0.0062 what is the conclusion (use a = 0.05)? a. The method has no effect. b. There is sufficient evidence to conclude that the method reduces the proportion of HIV positive patients who develop AIDS after four years. c. There is sufficient evidence to conclude that the method increases the proportion of HIV positive patients who develop AIDS after four years. d. There is insufficient evidence to conclude that the method reduces the proportion of HIV positive patients who develop AIDS after four years.Use the following information to answer the next two exercises. An experiment is conducted to show that blood pressure can be consciously reduced in people trained in a “biofeedback exercise program.” Six subjects were randomly selected and blood pressure measurements were recorded before and after the training. The difference between blood pressures was calculated (after - before) producing the following results: xd=10.2d=8.4 . Using the data, test the hypothesis that the blood pressure has decreased after the training. The distribution for the test is: a. t5 b. t6 c. N(10.2,8.4) d. N(10.2,8.466)Use the following information to answer the next two exercises. An experiment is conducted to show that blood pressure can be consciously reduced in people trained in a “biofeedback exercise program.” Six subjects were randomly selected and blood pressure measurements were recorded before and after the training. The difference between blood pressures was calculated (after - before) producing the following results: xd=10.2d=8.4 . Using the data, test the hypothesis that the blood pressure has decreased after the training. If a = 0.05, the p-value and the conclusion are a. 0.0014; There is sufficient evidence to conclude that the blood pressure decreased after the training. b. 0.0014; There is sufficient evidence to conclude that the blood pressure increased after the training. c. 0.0155; There is sufficient evidence to conclude that the blood pressure decreased after the training. d. 0.0155; There is sufficient evidence to conclude that the blood pressure increased after the training.A golf instructor is interested in determining if her new technique for improving players’ golf scores is effective. She takes four new students. She records their 18-hole scores before learning the technique and then after having taken her class. She conducts a hypothesis test. The data are as follows. Player 1 Player 2 Player 3 Player 4 Mean score before class 83 78 93 87 Mean score after class 80 80 86 86 Table 10.31 The correct decision is: a. RejectH0. b. Do not reject the H0.A local cancer support group believes that the estimate for new female breast cancer cases in the south is higher in 2013 than in 2012. The group compared the estimates of new female breast cancer cases by southern state in 2012 and in 2013. The results are in Table 10.32. Southern States 2012 2013 Alabama 3,450 3,720 Arkansas 2,150 2,280 Florida 15,540 15,710 Georgia 6,970 7,310 Kentucky 3,160 3,300 Louisiana 3,320 3,630 Mississippi 1,990 2,080 North Carolina 7,090 7,430 Oklahoma 2,630 2,690 South Carolina 3,570 3,580 Tennessee 4,680 5,070 Texas 15,050 14,980 Virginia 6,190 6,280 Table 10.32A traveler wanted to know if the prices of hotels are different in the ten cities that he visits the most often. The list of the cities with the corresponding hotel prices for his two favorite hotel chains is in Table 10.33. Test at the 1% level of significance. Cities Hyatt Regency prices in dollars Hilton prices in dollars Atlanta 107 169 Boston 358 289 Chicago 209 299 Dallas 209 198 Denver 167 169 Indianapolis 179 214 Los Angeles 179 169 New York City 625 459 Philadelphia 179 159 Washington, DC 245 239 Table 10.33A politician asked his staff to determine whether the underemployment rate in the northeast decreased from 2011 to 2012. The results are in Table 10.34. Northeastern States 2011 2012 Connecticut 17.3 16.4 Delaware 17.4 13.7 Maine 19.3 16.1 Maryland 16.0 15.5 Massachusetts 17.6 18.2 New Hampshire 15.4 13.5 New Jersey 19.2 18.7 New York 18.5 18.7 Ohio 18.2 18.8 Pennsylvania 16.5 16.9 Rhode Island 20.7 22.4 Vermont 14.7 12.3 West Virginia 15.5 17.3 Table 10.34A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. The population standard deviations are two pounds and three pounds, respectively. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet.A new chocolate bar is taste-tested on consumers. Of interest is whether the proportion of children who like the new chocolate bar is greater than the proportion of adults who like it.The mean number of English courses taken in a twoyear time period by male and female college students is believed to be about the same. An experiment is conducted and data are collected from nine males and 16 females.A football league reported that the mean number of touchdowns per game was five. A study is done to determine if the mean number of touchdowns has decreased.A study is done to determine if students in the California state university system take longer to graduate than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. From years of research, it is known that the population standard deviations are 1.5811 years and one year, respectively.According to a YWCA Rape Crisis Center newsletter, 75% of rape victims know their attackers. A study is done to verify this.According to a recent study, U.S. companies have a mean maternity-leave of six weeks.A recent drug survey showed an increase in use of drugs and alcohol among local high school students as compared to the national percent. Suppose that a survey of 100 local youths and 100 national youths is conducted to see if the proportion of drug and alcohol use is higher locally than nationally.A new SAT study course is tested on 12 individuals. Pre-course and post-course scores are recorded. Of interest is the mean increase in SAT scores. The following data are collected: Pre-course score Post-course score 1 300 960 920 1010 1100 840 880 1100 1070 1250 1320 860 860 1330 1370 790 770 990 1040 1110 1200 740 850 Table 10.35University of Michigan researchers reported in the Journal of the National Cancer Institute that quitting smoking is especially beneficial for those under age 49. In this American Cancer Society study, the risk (probability) of dying of lung cancer was about the same as for those who had never smoked.Lesley E. Tan investigated the relationship between left-handedness vs. right-handedness and motor competence in preschool children. Random samples of 41 left-handed preschool children and 41 right-handed preschool children were given several tests of motor skills to determine if there is evidence of a difference between the children based on this experiment. The experiment produced the means and standard deviations shown Table 10.36. Determine the appropriate test and best distribution to use for that test. Left-handed Right-handed Sample size 41 41 Sample mean 97.5 98.1 Sample standard deviation 17.5 19.2 Table 10.36 a. Two independent means, normal distribution b. Two independent means, Student’s-t distribution c. Matched or paired samples, Student’s-t distribution d. Two population proportions, normal distributionA golf instructor is interested in determining if her new technique for improving players’ golf scores is effective. She takes four (4) new students. She records their 18-hole scores before learning the technique and then after having taken her class. She conducts a hypothesis test. The data are as Table 10.37. Player 1 Player 2 Player 3 Player 4 Mean score before class 83 78 93 87 Mean score after class 80 80 86 86 Table 10.37 This is: a. a test of two independent means. b. a test of two proportions. c. a test of a single mean. d. a test of a single proportion.A factory manager needs to understand how many products are defective versus how many are produced. The number of expected defects is listed in Table 11.5. Number produced Number defective 1-100 5 101-200 6 201-300 7 301-400 8 401-500 10 Table 11.5 A random sample was taken to determine the actual number of defects. Table 11.6 shows the results of the survey. Number produced Number defective 1-100 5 101-200 7 201-300 8 301-400 9 401-500 11 Table 11.6 State the null and alternative hypotheses needed to conduct a goodness-of-fit test, and state the degrees of freedom.Teachers want to know which night each week their students are doing most of their homework. Most teachers think that students do homework equally throughout the week. Suppose a random sample of 56 students were asked on which night of the week they did the most homework. The results were distributed as in Table 11.8. Sunday Monday Tuesday Wednesday Thursday Friday Saturday Number of Students 11 8 10 7 10 5 5 Table 11.8 From the population of students, do the nights for the highest number of students doing the majority of their homework occur with equal frequencies during a week? What type of hypothesis test should you use?The expected percentage of the number of pets students have in their homes is distributed (this is the given distribution for the student population of the United States) as in Table 11.12. Number of Pets Percent 0 18 1 25 2 30 3 18 4+ 9 Table 11.12 A random sample of 1,000 students from the Eastern United States resulted in the data in Table 11.13. Number of Pets Frequency 0 210 1 240 2 320 3 140 4+ 90 Table 11.13 At the 1% significance level, does it appear that the distribution “number of pets” of students in the Eastern United States is different from the distribution for the United States student population as a whole? What is the p-value?Students in a social studies class hypothesize that the literacy rates across the world for every region are 82%. Table 11.14 shows the actual literacy rates across the world broken down by region. What are the test statistic and the degrees of freedom? MDG Region Adult Literacy Rate (%) Developed Regions 99.0 Commonwealth of Independent States 99.5 Northern Africa 67.3 Sub-Saharan Africa 62.5 Latin America and the Caribbean 91.0 Eastern Asia 93.8 Southern Asia 61.9 South-Eastern Asia 91.9 Western Asia 84.5 Oceania 66.4 Table 11.14A sample of 300 students is taken. Of the students surveyed, 50 were music students, while 250 were not. Ninetyseven were on the honor roll, while 203 were not. If we assume being a music student and being on the honor roll are independent events, what is the expected number of music students who are also on the honor roll?The Bureau of Labor Statistics gathers data about employment in the United States. A sample is taken to calculate the number of U.S. citizens working in one of several industry sectors over time. Table 11.17 shows the results: Industry Sector 2000 2010 2020 Total Nonagriculture wage and salary 13,243 13,044 15,018 41,305 Goods-producing, excluding agriculture 2,457 1,771 1,950 6,178 Services-providing 10,786 11,273 13,068 35,127 Agriculture, forestry, fishing, and hunting 240 214 201 655 Nonagriculture self-employed and unpaid family worker 931 894 972 2,797 Secondary wage and salary jobs in agriculture and private household Industries 14 11 11 36 Secondary jobs as a self-employed or unpaid family worker 196 144 152 492 Total 27,867 27,351 31,372 86,590 Table 11.17 We want to know if the change in the number of jobs is independent of the change in years. State the null and alternative hypotheses and the degrees of freedom.Refer back to the information in Try It. How many service providing jobs are there expected to be in 2020? How many nonagriculture wage and salary jobs are there expected to be in 2020?Do families and singles have the same distribution of cars? Use a level of significance of 0.05. Suppose that 100 randomly selected families and 200 randomly selected singles were asked what type of car they drove: sport, sedan, hatchback, truck, van/SUV. The results are shown in Table 11.20. Do families and singles have the same distribution of cars? Test at a level of significance of 0.05. Sport Sedan Hatchback Truck Van/SUV Family 5 15 35 17 28 Single 45 65 37 46 7 Table 11.20Ivy League schools receive many applications, but only some can be accepted. At the schools listed in Table 11.22, two types of applications are accepted: regular and early decision. Application Type Accepted Brown Columbia Cornell Dartmouth Penn Yale Regular 2,115 1,792 5,306 1,734 2,685 1,245 Early Decision 577 627 1,228 444 1,195 761 Table 11.22 We want to know if the number of regular applications accepted follows the same distribution as the number of early applications accepted. State the null and alternative hypotheses, the degrees of freedom and the test statistic, sketch the graph of the p-value, and draw a conclusion about the test of homogeneity.A SCUBA instructor wants to record the collective depths each of his students dives during their checkout. He is interested in how the depths vary, even though everyone should have been at the same depth. He believes the standard deviation is three feet. His assistant thinks the standard deviation is less than three feet. If the instructor were to conduct a test, what would the null and alternative hypotheses be?The FCC conducts broadband speed tests to measure how much data per second passes between a consumer’s computer and the internet. As of August of 2012, the standard deviation of Internet speeds across Internet Service Providers (ISPs) was 12.2 percent. Suppose a sample of 15 ISPs is taken, and the standard deviation is 13.2. An analyst claims that the standard deviation of speeds is more than what was reported. State the null and alternative hypotheses, compute the degrees of freedom, the test statistic, sketch the graph of the p-value, and draw a conclusion. Test at the1% significance level.If the number of degrees of freedom for a chi-square distribution is 25, what is the population mean and standard deviation?If df > 90, the distribution is _____________. If df = 15, the distribution is ________________.When does the chi-square curve approximate a normal distribution?Where is µ located on a chi-square curve?Is it more likely the df is 90, 20, or two in the graph? Figure 11.13Determine the appropriate test to be used in the next three exercises. An archeologist is calculating the distribution of the frequency of the number of artifacts she finds in a dig site. Based on previous digs, the archeologist creates an expected distribution broken down by grid sections in the dig site. Once the site has been fully excavated, she compares the actual number of artifacts found in each grid section to see if her expectation was accurate.Determine the appropriate test to be used in the next three exercises. An economist is deriving a model to predict outcomes on the stock market. He creates a list of expected points on the stock market index for the next two weeks. At the close of each day’s trading, he records the actual points on the index. He wants to see how well his model matched what actually happened.Determine the appropriate test to be used in the next three exercises. A personal trainer is putting together a weight-lifting program for her clients. For a 90-day program, she expects each client to lift a specific maximum weight each week. As she goes along, she records the actual maximum weights her clients lifted. She wants to know how well her expectations met with what was observed.Use the following information to answer the next five exercises: A teacher predicts that the distribution of grades on the final exam will be and they are recorded in Table 11.27. Grade Proportion A 0.25 B 0.30 C 0.35 D 0.10 The actual distribution for a class of 20 is in Table 11.28. Grade Frequency A 7 B 7 C 5 D 1 Table 11.28. d f = ______Use the following information to answer the next five exercises: A teacher predicts that the distribution of grades on the final exam will be and they are recorded in Table 11.27. Grade Proportion A 0.25 B 0.30 C 0.35 D 0.10 The actual distribution for a class of 20 is in Table 11.28. Grade Frequency A 7 B 7 C 5 D 1 Table 11.28. State the null and alternative hypotheses.x2test statistic = ______. Use the following information to answer the next five exercises: A teacher predicts that the distribution of grades on the final exam will be and they are recorded in Table 11.27. Grade Proportion A 0.25 B 0.30 C 0.35 D 0.10 The actual distribution for a class of 20 is in Table 11.28. Grade Frequency A 7 B 7 C 5 D 1 Table 11.28. 11. x2 test statistic = ______Use the following information to answer the next five exercises: A teacher predicts that the distribution of grades on the final exam will be and they are recorded in Table 11.27. Grade Proportion A 0.25 B 0.30 C 0.35 D 0.10 The actual distribution for a class of 20 is in Table 11.28. Grade Frequency A 7 B 7 C 5 D 1 Table 11.28. p-value = ______Use the following information to answer the next five exercises: A teacher predicts that the distribution of grades on the final exam will be and they are recorded in Table 11.27. Grade Proportion A 0.25 B 0.30 C 0.35 D 0.10 The actual distribution for a class of 20 is in Table 11.28. Grade Frequency A 7 B 7 C 5 D 1 Table 11.28. At the 5% significance level, what can you conclude?Use the following information to answer the next nine exercises: The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in Table 11.29. Ethnicity Number of Cases White 2,229 Hispanic 1,157 Black/African-American 457 Asian, Pacific Islander 232 Total = 4075 The percentage of each ethnic group in Santa Clara County is as in Table 11.30. Ethnicity Percentage of total county population Number expected (round to two decimal places) White 42.9% 1748.18 Hispanic 26.7% Black/African-American 2.6% Asian, Pacific Islander 27.8% Total=100% If the ethnicities of AIDS victims followed the ethnicities of the total county population, fill in the expected number of cases per ethnic group. Perform a goodness-of-fit test to determine whether the occurrence of AIDS cases follows the ethnicities of the general population of Santa Clara CountyUse the following information to answer the next nine exercises: The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in Table 11.29. Ethnicity Number of Cases White 2,229 Hispanic 1,157 Black/African-American 457 Asian, Pacific Islander 232 Total = 4075 The percentage of each ethnic group in Santa Clara County is as in Table 11.30. Ethnicity Percentage of total county population Number expected (round to two decimal places) White 42.9% 1748.18 Hispanic 26.7% Black/African-American 2.6% Asian, Pacific Islander 27.8% Total=100% H0: _______Use the following information to answer the next nine exercises: The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in Table 11.29. Ethnicity Number of Cases White 2,229 Hispanic 1,157 Black/African-American 457 Asian, Pacific Islander 232 Total = 4075 The percentage of each ethnic group in Santa Clara County is as in Table 11.30. Ethnicity Percentage of total county population Number expected (round to two decimal places) White 42.9% 1748.18 Hispanic 26.7% Black/African-American 2.6% Asian, Pacific Islander 27.8% Total=100% Ha: _______Use the following information to answer the next nine exercises: The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in Table 11.29. Ethnicity Number of Cases White 2,229 Hispanic 1,157 Black/African-American 457 Asian, Pacific Islander 232 Total = 4075 The percentage of each ethnic group in Santa Clara County is as in Table 11.30. Ethnicity Percentage of total county population Number expected (round to two decimal places) White 42.9% 1748.18 Hispanic 26.7% Black/African-American 2.6% Asian, Pacific Islander 27.8% Total=100% Is this a right-tailed, left-tailed, or two-tailed test?Use the following information to answer the next nine exercises: The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in Table 11.29. Ethnicity Number of Cases White 2,229 Hispanic 1,157 Black/African-American 457 Asian, Pacific Islander 232 Total = 4075 The percentage of each ethnic group in Santa Clara County is as in Table 11.30. Ethnicity Percentage of total county population Number expected (round to two decimal places) White 42.9% 1748.18 Hispanic 26.7% Black/African-American 2.6% Asian, Pacific Islander 27.8% Total=100% degrees of freedom = _______Use the following information to answer the next nine exercises: The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in Table 11.29. Ethnicity Number of Cases White 2,229 Hispanic 1,157 Black/African-American 457 Asian, Pacific Islander 232 Total = 4075 The percentage of each ethnic group in Santa Clara County is as in Table 11.30. Ethnicity Percentage of total county population Number expected (round to two decimal places) White 42.9% 1748.18 Hispanic 26.7% Black/African-American 2.6% Asian, Pacific Islander 27.8% Total=100% 2 test statistic = _______Use the following information to answer the next nine exercises: The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in Table 11.29. Ethnicity Number of Cases White 2,229 Hispanic 1,157 Black/African-American 457 Asian, Pacific Islander 232 Total = 4075 The percentage of each ethnic group in Santa Clara County is as in Table 11.30. Ethnicity Percentage of total county population Number expected (round to two decimal places) White 42.9% 1748.18 Hispanic 26.7% Black/African-American 2.6% Asian, Pacific Islander 27.8% Total=100% p-value = _______Use the following information to answer the next nine exercises: The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in Table 11.29. Ethnicity Number of Cases White 2,229 Hispanic 1,157 Black/African-American 457 Asian, Pacific Islander 232 Total = 4075 The percentage of each ethnic group in Santa Clara County is as in Table 11.30. Ethnicity Percentage of total county population Number expected (round to two decimal places) White 42.9% 1748.18 Hispanic 26.7% Black/African-American 2.6% Asian, Pacific Islander 27.8% Total=100% Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade in the region corresponding to the p-value. Figure 11.14 Let a = 0.05 Decision: ________________ Reason for the Decision: ________________ Conclusion (write out in complete sentences): ________________Use the following information to answer the next nine exercises: The following data are real. The cumulative number of AIDS cases reported for Santa Clara County is broken down by ethnicity as in Table 11.29. Ethnicity Number of Cases White 2,229 Hispanic 1,157 Black/African-American 457 Asian, Pacific Islander 232 Total = 4075 The percentage of each ethnic group in Santa Clara County is as in Table 11.30. Ethnicity Percentage of total county population Number expected (round to two decimal places) White 42.9% 1748.18 Hispanic 26.7% Black/African-American 2.6% Asian, Pacific Islander 27.8% Total=100% Does it appear that the pattern of AIDS cases in Santa Clara County corresponds to the distribution of ethnic groups in this county? Why or why not?Test of Independence Determine the appropriate test to be used in the next three exercises. A pharmaceutical company is interested in the relationship between age and presentation of symptoms for a common viral infection. A random sample is taken of 500 people with the infection across different age groups.Test of Independence Determine the appropriate test to be used in the next three exercises. The owner of a baseball team is interested in the relationship between player salaries and team winning percentage. He takes a random sample of 100 players from different organizations.Test of Independence Determine the appropriate test to be used in the next three exercises. A marathon runner is interested in the relationship between the brand of shoes runners wear and their run times. She takes a random sample of 50 runners and records their run times as well as the brand of shoes they were wearing.Use the following information to answer the next seven exercises: Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken. Table 11.31 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel. Traveling Distance Third class Second class First class Total 1100 miles 21 14 6 41 101200 miles 18 16 8 42 201300 miles 16 17 15 48 301400 miles 12.00% 14 21 47 401500 miles 6 6 10 22 Total 73 67 60 200 Table 11.31 State the hypotheses. H0: _______ Ha: _______Use the following information to answer the next seven exercises: Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken. Table 11.31 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel. Traveling Distance Third class Second class First class Total 1100 miles 21 14 6 41 101200 miles 18 16 8 42 201300 miles 16 17 15 48 301400 miles 12.00% 14 21 47 401500 miles 6 6 10 22 Total 73 67 60 200 Table 11.31 df = _______Use the following information to answer the next seven exercises: Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken. Table 11.31 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel. Traveling Distance Third class Second class First class Total 1100 miles 21 14 6 41 101200 miles 18 16 8 42 201300 miles 16 17 15 48 301400 miles 12.00% 14 21 47 401500 miles 6 6 10 22 Total 73 67 60 200 Table 11.31 How many passengers are expected to travel between 201 and 300 miles and purchase second-class tickets?Use the following information to answer the next seven exercises: Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken. Table 11.31 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel. Traveling Distance Third class Second class First class Total 1100 miles 21 14 6 41 101200 miles 18 16 8 42 201300 miles 16 17 15 48 301400 miles 12.00% 14 21 47 401500 miles 6 6 10 22 Total 73 67 60 200 Table 11.31 How many passengers are expected to travel between 401 and 500 miles and purchase first-class tickets?Use the following information to answer the next seven exercises: Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken. Table 11.31 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel. Traveling Distance Third class Second class First class Total 1100 miles 21 14 6 41 101200 miles 18 16 8 42 201300 miles 16 17 15 48 301400 miles 12.00% 14 21 47 401500 miles 6 6 10 22 Total 73 67 60 200 Table 11.31 What is the test statistic?Use the following information to answer the next seven exercises: Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken. Table 11.31 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel. Traveling Distance Third class Second class First class Total 1100 miles 21 14 6 41 101200 miles 18 16 8 42 201300 miles 16 17 15 48 301400 miles 12.00% 14 21 47 401500 miles 6 6 10 22 Total 73 67 60 200 Table 11.31 What is the p-value?Use the following information to answer the next seven exercises: Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken. Table 11.31 shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance they must travel. Traveling Distance Third class Second class First class Total 1100 miles 21 14 6 41 101200 miles 18 16 8 42 201300 miles 16 17 15 48 301400 miles 12.00% 14 21 47 401500 miles 6 6 10 22 Total 73 67 60 200 Table 11.31 What can you conclude at the 5% level of significance?Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans and 7,650 whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites. Complete the table. Smoking Level Per Day African 'American Native Hawaiian Latino Japanese Americans White TOTALS 1-10 11-20 21-30 31+ TOTALS Table 11.32 Smoking Levels by Ethnicity (Observed)Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans and 7,650 whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites. State the hypotheses. H0: _______ Ha: _______Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans and 7,650 whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites. 35. Enter expected values in Table 11.32. Round to two decimal places. Calculate the following values:Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans and 7,650 whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites. df = _______Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans and 7,650 whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites. 2test statistic = ______Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans and 7,650 whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites. p-value = ______Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans and 7,650 whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites. Is this a right-tailed, left-tailed, or two-tailed test? Explain why.Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans and 7,650 whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites. Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade in the region corresponding to the p-value. Figure 11.15 State the decision and conclusion (in a complete sentence) for the following preconceived levels of a.a = 0.05 a. Decision: ___________________ b. Reason for the decision: ___________________ c. Conclusion (write out in a complete sentence): ___________________a = 0.01 a. Decision: ___________________ b. Reason for the decision: ___________________ c. Conclusion (write out in a complete sentence): ___________________A math teacher wants to see if two of her classes have the same distribution of test scores. What test should she use?What are the null and alternative hypotheses for Exercise 11.43?A market researcher wants to see if two different stores have the same distribution of sales throughout the year. What type of test should he use?A meteorologist wants to know if East and West Australia have the same distribution of storms. What type of test should she use?What condition must be met to use the test for homogeneity?Use the following information to answer the next five exercises: Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table 11.33. 20-30 30-40 40-50 50-60 Private Practice 16 40 38 6 Hospital 8 44 59 39 Table 11.33 State the null and alternative hypotheses.Use the following information to answer the next five exercises: Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table 11.33. 20-30 30-40 40-50 50-60 Private Practice 16 40 38 6 Hospital 8 44 59 39 Table 11.33 df = _______Use the following information to answer the next five exercises: Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table 11.33. 20-30 30-40 40-50 50-60 Private Practice 16 40 38 6 Hospital 8 44 59 39 Table 11.33 What is the test statistic?Use the following information to answer the next five exercises: Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table 11.33. 20-30 30-40 40-50 50-60 Private Practice 16 40 38 6 Hospital 8 44 59 39 Table 11.33 What is the p-value?Use the following information to answer the next five exercises: Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in Table 11.33. 20-30 30-40 40-50 50-60 Private Practice 16 40 38 6 Hospital 8 44 59 39 Table 11.33 What can you conclude at the 5% significance level?Which test do you use to decide whether an observed distribution is the same as an expected distribution?What is the null hypothesis for the type of test from Exercise 11.53?Which test would you use to decide whether two factors have a relationship?Which test would you use to decide if two populations have the same distribution?How are tests of independence similar to tests for homogeneity?How are tests of independence different from tests for homogeneity?Test of a Single Variance Use the following information to answer the next three exercises: An archer’s standard deviation for his hits is six (data is measured in distance from the center of the target). An observer claims the standard deviation is less. What type of test should be used?Test of a Single Variance Use the following information to answer the next three exercises: An archer’s standard deviation for his hits is six (data is measured in distance from the center of the target). An observer claims the standard deviation is less. 60. State the null and alternative hypotheses.Test of a Single Variance Use the following information to answer the next three exercises: An archer’s standard deviation for his hits is six (data is measured in distance from the center of the target). An observer claims the standard deviation is less. Is this a right-tailed, left-tailed, or two-tailed test?Use the following information to answer the next three exercises: The standard deviation of heights for students in a school is 0.81. A random sample of 50 students is taken, and the standard deviation of heights of the sample is 0.96. A researcher in charge of the study believes the standard deviation of heights for the school is greater than 0.81. What type of test should be used?Use the following information to answer the next three exercises: The standard deviation of heights for students in a school is 0.81. A random sample of 50 students is taken, and the standard deviation of heights of the sample is 0.96. A researcher in charge of the study believes the standard deviation of heights for the school is greater than 0.81. State the null and alternative hypotheses.Use the following information to answer the next three exercises: The standard deviation of heights for students in a school is 0.81. A random sample of 50 students is taken, and the standard deviation of heights of the sample is 0.96. A researcher in charge of the study believes the standard deviation of heights for the school is greater than 0.81. df = ________Use the following information to answer the next four exercises: The average waiting time in a doctor’s office varies. The standard deviation of waiting times in a doctor’s office is 3.4 minutes. A random sample of 30 patients in the doctors office has a standard deviation of waiting times of 4.1 minutes. One doctor believes the variance of waiting times is greater than originally thought. What type of test should be used?Use the following information to answer the next four exercises: The average waiting time in a doctors office varies. The standard deviation of waiting times in a doctors office is 3.4 minutes. A random sample of 30 patients in the doctors office has a standard deviation of waiting times of 4.1 minutes. One doctor believes the variance of waiting times is greater than originally thought. What is the test statistic?Use the following information to answer the next four exercises: The average waiting time in a doctor’s office varies. The standard deviation of waiting times in a doctor’s office is 3.4 minutes. A random sample of 30 patients in the doctor’s office has a standard deviation of waiting times of 4.1 minutes. One doctor believes the variance of waiting times is greater than originally thought. What is the p-value?Use the following information to answer the next four exercises: The average waiting time in a doctor’s office varies. The standard deviation of waiting times in a doctor’s office is 3.4 minutes. A random sample of 30 patients in the doctor’s office has a standard deviation of waiting times of 4.1 minutes. One doctor believes the variance of waiting times is greater than originally thought. What can you conclude at the 5% significance level?As the number of degrees of freedom increases, the graph of the chi-square distribution looks more and more Symmetrical.The standard deviation of the chi-square distribution is twice the mean.The mean and the median of the chi-square distribution are the same if df = 24.A six-sided die is rolled 120 times. Fill in the expected frequency column. Then, conduct a hypothesis test to determine if the die is fair. The data in Table 11.34 are the result of the 120 rolls. Face Value Frequency Expected Frequency 1 15 2 29 3 16 4 15 5 30 6 15 Table 11.34The marital status distribution of the U.S. male population, ages 15 and older, is as shown in Table 11.35. Marital Status Percent Expected Frequency Marital Status Percent Expected Frequency never married 31.3 married 56.1 widowed 2.5 divorced/separated 10.1 Table 11.35 Suppose that a random sample of 400 U.S. young adult males, 18 to 24 years old, yielded the following frequency distribution. We are interested in whether this age group of males fits the distribution of the U.S. adult population. Calculate the frequency one would expect when surveying 400 people. Fill in Table 11.35, rounding to two decimal places. Marital Status Frequency Marital Status Expected Frequency never married 140 married 238 widowed 2 divorced/separated 20 Table 11.36Use the following information to answer the next two exercises: The columns in Table 11.37 contain the Race/Ethnicity of U.S. Public Schools for a recent year, the percentages for the Advanced Placement Examinee Population for that class, and the Overall Student Population. Suppose the right column contains the result of a survey of 1,000 local students from that year who took an AP Exam. Race/Ethnicity AP Examinee Population Overall Student Population Survey Frequency Asian, Asian American, or Pacific Islander 10.20% 5.40% 113 Black or African-American 8.20% 14.50% 94 Hispanic or Latino 15.50% 15.90% 136 American Indian or Alaska Native 0.60% 1.20% 10 White 59.40% 61.60% 604 Not reported/other 6.10% 1.40% 43 Table 11.37 Perform a goodness-of-fit test to determine whether the local results follow the distribution of the U.S. overall student population based on ethnicity.Use the following information to answer the next two exercises: The columns in Table 11.37 contain the Race/Ethnicity of U.S. Public Schools for a recent year, the percentages for the Advanced Placement Examinee Population for that class, and the Overall Student Population. Suppose the right column contains the result of a survey of 1,000 local students from that year who took an AP Exam. Race/Ethnicity AP Examinee Population Overall Student Population Survey Frequency Asian, Asian American, or Pacific Islander 10.20% 5.40% 113 Black or African-American 8.20% 14.50% 94 Hispanic or Latino 15.50% 15.90% 136 American Indian or Alaska Native 0.60% 1.20% 10 White 59.40% 61.60% 604 Not reported/other 6.10% 1.40% 43 Table 11.37 Perform a goodness-of-fit test to determine whether the local results follow the distribution of U.S. AP examinee population, based on ethnicity.The City of South Lake Tahoe, CA, has an Asian population of 1,419 people, out of a total population of 23,609.Suppose that a survey of 1,419 self-reported Asians in the Manhattan, NY, area yielded the data in Table 11.38. Conduct a goodness-of-fit test to determine if the self-reported sub-groups of Asians in the Manhattan area fit that of the Lake Tahoe area. Race Lake Tahoe Frequency Manhattan Frequency Asian Indian 131 174 Chinese 118 557 Filipino 1,045 518 Japanese 80 54 Korean 12 29 Vietnamese 9 21 Other 24 66 Table 11.38Use the following information to answer the next two exercises: UCLA conducted a survey of more than 263,000 college freshmen from 385 colleges in fall 2005. The results of students' expected majors by gender were reported in The Chronicle of Higher Education (2/2/2006). Suppose a survey of 5,000 graduating females and 5,000 graduating males was done as a follow-up last year to determine what their actual majors were. The results are shown in the tables for Exercise 11.77 and Exercise 11.78. The second column in each table does not add to 100% because of rounding. Conduct a goodness-of-fit test to determine if the actual college majors of graduating females fit the distribution of their expected majors. Major Women - Expected Major Women - Actual Major Arts & Humanities 14.0% 670 Biological Sciences 8.4% 410 Business 13.1% 685 Education 13.0% 650 Engineering 2.6% 145 Physical Sciences 2.6% 125 Professional 18.9% 975 Social Sciences 13.0% 605 Technical 0.4% 15 Other 5.8% 300 Undecided 8.0% 420 Table 11.39Use the following information to answer the next two exercises: UCLA conducted a survey of more than 263,000 college freshmen from 385 colleges in fall 2005. The results of students' expected majors by gender were reported in The Chronicle of Higher Education (2/2/2006). Suppose a survey of 5,000 graduating females and 5,000 graduating males was done as a follow-up last year to determine what their actual majors were. The results are shown in the tables for Exercise 11.77 and Exercise 11.78. The second column in each table does not add to 100% because of rounding. Conduct a goodness-of-fit test to determine if the actual college majors of graduating males fit the distribution of their expected majors. Major Women - Expected Major Women - Actual Major Arts & Humanities 11.0% 600 Biological Sciences 6.7% 330 Business 22.7% 1130 Education 5.8% 305 Engineering 15.6% 800 Physical Sciences 3.6% 175 Professional 9.3% 460 Social Sciences 7.6% 370 Technical 1.8% 90 Other 8.2% 400 Undecided 6.6% 340 Table 11.40 Read the statement and decide whether it is true or false.In a goodness-of-fit test, the expected values are the values we would expect if the null hypothesis were true.In general, if the observed values and expected values of a goodness-of-fit test are not close together, then the teststatistic can get very large and on a graph will be way out in the right tail.Use a goodness-of-fit test to determine if high school principals believe that students are absent equally during the week or not.The test to use to determine if a six-sided die is fair is a goodness-of-fit test.In a goodness-of fit test, if the p-value is 0.0113, in general, do not reject the null hypothesis.A sample of 212 commercial businesses was surveyed for recycling one commodity; a commodity here means any one type of recyclable material such as plastic or aluminum. Table 11.41 shows the business categories in the survey, the sample size of each category, and the number of businesses in each category that recycle one commodity. Based on the study, on average half of the businesses were expected to be recycling one commodity. As a result, the last column shows the expected number of businesses in each category that recycle one commodity. At the 5% significance level, perform a hypothesis test to determine if the observed number of businesses that recycle one commodity follows the uniform distribution of the expected values. BusinessType Number inclass Observed Number that recycleone commodity Expected number that recycleone commodity Office 35 19 17.5 Retail/ Wholesale 48 27 24 Food/ Restaurants 53 35 26.5 Manufacturing/ Medical 52 21 26 Hotel/Mixed 24 9 12 Table 11.41Table 11.42 contains information from a survey among 499 participants classified according to their age groups. The second column shows the percentage of obese people per age class among the study participants. The last column comes from a different study at the national level that shows the corresponding percentages of obese people in the same age classes in the USA. Perform a hypothesis test at the 5% significance level to determine whether the survey participants are a representative sample of the USA obese population. Age Class (Years) Obese Expected (Percentage) Observed Number that recycle one commodity Obese-Observed (Frequencies) 2030 22.4 122 17.5 3140 18.6 104 24 4150 12.8 78 26.5 5160 10.4 64 26 6170 35.8 168 12 Table 11.42A recent debate about where in the United States skiers believe the skiing is best prompted the following survey. Testto see if the best ski area is independent of the level of the skier. U.S. Ski Area Beginner Intermediate Advanced Tahoe 20 30 40 Utah 10 30 60 Colorado 10 40 50 Table 11.43Car manufacturers are interested in whether there is a relationship between the size of car an individual drives and the number of people in the driver’s family (that is, whether car size and family size are independent). To test this, suppose that800 car owners were randomly surveyed with the results in Table 11.44. Conduct a test of independence. Family Size Sub & Compact Mid-size Full-size Van & Truck 1 20 35 40 35 2 20 50 70 80 3-4 20 50 100 90 5+ 20 30 70 70 Table 11.44College students may be interested in whether or not their majors have any effect on starting salaries after graduation. Suppose that 300 recent graduates were surveyed as to their majors in college and their starting salaries after graduation. Table 11.45 shows the data. Conduct a test of independence. Major < $50,000 $50,000 $50,000 $68,999 $69,000 + English 5 20 5 Engineering 10 30 60 Nursing 10 15 15 Business 10 20 30 Psychology 20 30 20 Table 11.45Some travel agents claim that honeymoon hot spots vary according to age of the bride. Suppose that 280 recent brides were interviewed as to where they spent their honeymoons. The information is given in Table 11.46. Conduct a test of independence. Location 20-29 30-39 40-50 50 and over Niagara Falls 15 25 25 20 Poconos 15 25 25 10 Europe 10 25 15 5 Virgin Islands 20 25 15 5 Table 11.46A manager of a sports club keeps information concerning the main sport in which members participate and their ages. To test whether there is a relationship between the age of a member and his or her choice of sport, 643 members of the sports club are randomly selected. Conduct a test of independence. Sport 18-25 26-30 31-40 41 and over racquetball 42 58 30 46 tennis 58 76 38 65 swimming 72 60 65 33 Table 11.47A major food manufacturer is concerned that the sales for its skinny french fries have been decreasing. As a part of a feasibility study, the company conducts research into the types of fries sold across the country to determine if the type of fries sold is independent of the area of the country. The results of the study are shown in Table 11.48. Conduct a test of independence. Type of Fries Northeast South Central West skinny fries 70 50 20 25 curly fries 100 60 15 30 steak fries 20 40 10 10 Table 11.48According to Dan Lenard, an independent insurance agent in the Buffalo, N.Y. area, the following is a breakdown of the amount of life insurance purchased by males in the following age groups. He is interested in whether the age of the male and the amount of life insurance purchased are independent events. Conduct a test for independence. Age of Males None < $200,000 $200,000$400,000 $401,001$1,000,000 $1,000,001+ 20-29 40 15 40 0 5 30-39 35 5 20 20 10 40-49 20 0 30 0 30 50+ 40 30 15 15 10 Table 11.49Suppose that 600 thirty-year-olds were surveyed to determine whether or not there is a relationship between the level of education an individual has and salary. Conduct a test of independence. AnnualSalary Not a high schoolgraduate High schoolgraduate Collegegraduate Masters ordoctorate < $30,000 15 25 10 5 $30,000$40,000 20 40 70 30 $40,000$50,000 10 20 40 55 $50,000$60,000 5 10 20 60 $60,000+ 0 5 10 150The number of degrees of freedom for a test of independence is equal to the sample size minus one.The test for independence uses tables of observed and expected data valuesThe test to use when determining if the college or university a student chooses to attend is related to his or her socioeconomic status is a test for independence.In a test of independence, the expected number is equal to the row total multiplied by the column total divided by the total surveyed.An ice cream maker performs a nationwide survey about favorite flavors of ice cream in different geographic areas of the U.S. Based on Table 11.51, do the numbers suggest that geographic location is independent of favorite ice cream flavors? Test at the 5% significance level. U.S. region/Flavor Strawberry Chocolate Vanilla RockyRoad MintChocolateChip Pistachio Rowtotal West 12 21 22 19 15 8 97 Midwest 10 32 22 11 15 6 96 East 8 31 27 8 15 7 96 South 15 28 30 8 15 6 102 Column Total 45 112 101 46 60 27 391 Table 11.51Table 11.52 provides a recent survey of the youngest online entrepreneurs whose net worth is estimated at one million dollars or more. Their ages range from 17 to 30. Each cell in the table illustrates the number of entrepreneurs who correspond to the specific age group and their net worth. Are the ages and net worth independent? Perform a test of independence at the 5% significance level. Age Group\ Net Worth Value (in millions of US dollars) 6-Jan 24-Jun >25 Row Total 17-25 8 7 5 20 26-30 6 5 9 20 Column Total 14 12 14 40 Table 11.52A 2013 poll in California surveyed people about taxing sugar-sweetened beverages. The results are presented in Table11.53, and are classified by ethnic group and response type. Are the poll responses independent of the participants’ ethnic group? Conduct a test of independence at the 5% significance level. Opinion/Ethnicity Asian-American White/Non-Hispanic African-American Latino Row Total Against tax 48 433 41 160 682 In Favor of tax 54 234 24 147 459 No opinion 16 43 16 19 94 Column Total 118 710 81 326 1235 Table 11.53A psychologist is interested in testing whether there is a difference in the distribution of personality types for business majors and social science majors. The results of the study are shown in Table 11.54. Conduct a test of homogeneity. Test at a 5% level of significance. Open Conscientious Extrovert Extrovert Neurotic Business 41 52 46 61 58 Social Science 72 75 63 80 65 Table 11.54Do men and women select different breakfasts? The breakfasts ordered by randomly selected men and women at a popular breakfast place is shown in Table 11.55. Conduct a test for homogeneity at a 5% level of significance. French Toast Pancakes Waffles Omelettes Men 47 35 28 53 Women 65 59 55 60 Table 11.55A fisherman is interested in whether the distribution of fish caught in Green Valley Lake is the same as the distribution of fish caught in Echo Lake. Of the 191 randomly selected fish caught in Green Valley Lake, 105 were rainbow trout, 27 were other trout, 35 were bass, and 24 were catfish. Of the 293 randomly selected fish caught in Echo Lake, 115 were rainbow trout, 58 were other trout, 67 were bass, and 53 were catfish. Perform a test for homogeneity at a 5% level of significance.In 2007, the United States had 1.5 million homeschooled students, according to the U.S. National Center for Education Statistics. In Table 11.56 you can see that parents decide to homeschool their children for different reasons, and some reasons are ranked by parents as more important than others. According to the survey results shown in the table, is the distribution of applicable reasons the same as the distribution of the most important reason? Provide your assessment at the 5% significance level. Did you expect the result you obtained? Reasons forHomeschooling Applicable Reason (inthousands ofrespondents) Most Important Reason(in thousands ofrespondents) RowTotal Concern about the environment of other schools 1,321 309 1,630 Dissatisfaction with academic instruction at other schools 1,096 258 1,354 To provide religious or moral instruction 1,257 540 1,797 Child has special needs, other than physical or mental 315 55 370 Nontraditional approach to child’s education 984 99 1,083 Nontraditional approach to child’s education 485 216 701 Column Total 5,458 1,477 6,935 Table 11.56When looking at energy consumption, we are often interested in detecting trends over time and how they correlate among different countries. The information in Table 11.57 shows the average energy use (in units of kg of oil equivalent per capita) in the USA and the joint European Union countries (EU) for the six-year period 2005 to 2010. Do the energy use values in these two areas come from the same distribution? Perform the analysis at the 5% significance level. Year European Union United States Row Total 2,010 3,413 7,164 10,557 2,009 3,302 7,057 10,359 2,008 3,505 7,488 10,993 2,007 3,537 7,758 11,295 2,006 3,595 7,697 11,292 2,005 3,613 7,847 11,460 Column Total 20,965 45,011 65,976 Table 11.57The Insurance Institute for Highway Safety collects safety information about all types of cars every year, and publishes a report of Top Safety Picks among all cars, makes, and models. Table 11.58 presents the number of Top Safety Picks in six car categories for the two years 2009 and 2013. Analyze the table data to conclude whether the distribution of cars that earned the Top Safety Picks safety award has remained the same between 2009 and 2013. Derive your results at the 5% significance level. Year \ CarType Small Mid-Size Large SmallSUV Mid-SizeSUV LargeSUV RowTotal 2,009 12 22 10 10 27 6 87 2,013 31 30 19 11 29 4 124 Column Total 43 52 29 21 56 10 211 Table 11.58Is there a difference between the distribution of community college statistics students and the distribution of university statistics students in what technology they use on their homework? Of some randomly selected community college students, 43 used a computer, 102 used a calculator with built in statistics functions, and 65 used a table from the textbook. Of some randomly selected university students, 28 used a computer, 33 used a calculator with built in statistics functions, and 40 used a table from the textbook. Conduct an appropriate hypothesis test using a 0.05 level of significance. Read the statement and decide whether it is true or false.If df = 2, the chi-square distribution has a shape that reminds us of the exponential.Test of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. Is the traveler disputing the claim about the average or about the variance?Test of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. A sample standard deviation of 15 minutes is the same as a sample variance of __________ minutes.Test of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. Is this a right-tailed, left-tailed, or two-tailed test?Test of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. H0: __________Test of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. df = ________Test of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. chi-square test statistic = ________Test of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. p-value = ________Test of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. Graph the situation. Label and scale the horizontal axis. Mark the mean and test statistic. Shade the p-value.Test of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. Let a = 0.05 Decision: ________ Conclusion (write out in a complete sentence.): ________Test of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. How did you know to test the variance instead of the mean?Test of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. If an additional test were done on the claim of the average delayTest of a Single Variance Use the following information to answer the next twelve exercises: Suppose an airline claims that its flights are consistently on time with an average delay of at most 15 minutes. It claims that the average delay is so consistent that the variance is no more than 150 minutes. Doubting the consistency part of the claim, a disgruntled traveler calculates the delays for his next 25 flights. The average delay for those 25 flights is 22 minutes with a standard deviation of 15 minutes. If an additional test were done on the claim of the average delay, but 45 flights were surveyed, which distribution would you use?A plant manager is concerned her equipment may need recalibrating. It seems that the actual weight of the 15 oz. cereal boxes it fills has been fluctuating. The standard deviation should be at most 0.5 oz. In order to determine if the machine needs to be recalibrated, 84 randomly selected boxes of cereal from the next day’s production were weighed. The standard deviation of the 84 boxes was 0.54. Does the machine need to be recalibrated?Consumers may be interested in whether the cost of a particular calculator varies from store to store. Based on surveying 43 stores, which yielded a sample mean of $84 and a sample standard deviation of $12, test the claim that the standard deviation is greater than $15.Isabella, an accomplished Bay to Breakers runner, claims that the standard deviation for her time to run the 7.5 mile race is at most three minutes. To test her claim, Rupinder looks up five of her race times. They are 55 minutes, 61 minutes,58 minutes, 63 minutes, and 57 minutes.Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. They are also interested in the variation of the number of babies. Suppose that an airline executive believes the average number of babies on flights is six with a variance of nine at most. The airline conducts a survey. The results of the 18 flights surveyed give a sample average of 6.4 with a sample standard deviation of 3.9. Conduct a hypothesis test of the airline executive’s belief.The number of births per woman in China is 1.6 down from 5.91 in 1966. This fertility rate has been attributed to the law passed in 1979 restricting births to one per woman. Suppose that a group of students studied whether or not the standard deviation of births per woman was greater than 0.75. They asked 50 women across China the number of births they had had. The results are shown in Table 11.59. Does the students’ survey indicate that the standard deviation is greater than 0.75? # of births Frequency 0 5 1 30 2 10 3 5 Table 11.59According to an avid aquarist, the average number of fish in a 20-gallon tank is 10, with a standard deviation of two. His friend, also an aquarist, does not believe that the standard deviation is two. She counts the number of fish in 15 other 20-gallon tanks. Based on the results that follow, do you think that the standard deviation is different from two? Data: 11; 10; 9; 10; 10; 11; 11; 10; 12; 9; 7; 9; 11; 10; 11The manager of "Frenchies" is concerned that patrons are not consistently receiving the same amount of French fries with each order. The chef claims that the standard deviation for a ten-ounce order of fries is at most 1.5 oz., but the manager thinks that it may be higher. He randomly weighs 49 orders of fries, which yields a mean of 11 oz. and a standard deviation of two oz.You want to buy a specific computer. A sales representative of the manufacturer claims that retail stores sell this computer at an average price of $1,249 with a very narrow standard deviation of $25. You find a website that has a price comparison for the same computer at a series of stores as follows: $1,299; $1,229.99; $1,193.08; $1,279; $1,224.95; $1,229.99; $1,269.95; $1,249. Can you argue that pricing has a larger standard deviation than claimed by the manufacturer? Use the 5% significance level. As a potential buyer, what would be the practical conclusion from your analysis?A company packages apples by weight. One of the weight grades is Class A apples. Class A apples have a mean weight of 150 g, and there is a maximum allowed weight tolerance of 5% above or below the mean for apples in the same consumer package. A batch of apples is selected to be included in a Class A apple package. Given the following apple weights of the batch, does the fruit comply with the Class A grade weight tolerance requirements. Conduct an appropriate hypothesis test. (a) at the 5% significance level (b) at the 1% significance level Weights in selected apple batch (in grams): 158; 167; 149; 169; 164; 139; 154; 150; 157; 171; 152; 161; 141; 166; 172;a. Explain why a goodness-of-fit test and a test of independence are generally right-tailed tests. b. If you did a left-tailed test, what would you be testing?Is the following an example of a linear equation? y=0.1253.5xIs the following an example of a linear equation? Why or why not? Figure 12.3 Example 12.3Emma’s Extreme Sports hires hang-gliding instructors and pays them a fee of $50 per class as well as $20 per student in the class. The total cost Emma pays depends on the number of students in a class. Find the equation that expresses the total cost in terms of the number of students in a class.Ethan repairs household appliances like dishwashers and refrigerators. For each visit, he charges $25 plus $20 per hour of work. A linear equation that expresses the total amount of money Ethan earns per visit is y = 25 + 20x. What are the independent and dependent variables? What is the y-intercept and what is the slope? Interpret them using complete sentences.Amelia plays basketball for her high school. She wants to improve to play at the college level. She notices that the number of points she scores in a game goes up in response to the number of hours she practices her jump shot each week. She records the following data: Chapter 12 | Linear Regression and Correlation 683 X (hours practicing jump shot) Y (points scored in a game) 5 15 7 22 9 28 10 31 11 33 12 36 Table 12.2 Construct a scatter plot and state if what Amelia thinks appears to be true.SCUBA divers have maximum dive times they cannot exceed when going to different depths. The data in Table 12.4 show different depths with the maximum dive times in minutes. Use your calculator to find the least squares regression line and predict the maximum dive time for 110 feet. X (depth in feet) Y (maximum dive time) 50 80 60 55 70 45 80 35 90 25 100 22 Table 12.4For a given line of best fit, you computed that r = 0.6501 using n = 12 data points and the critical value is 0.576. Can the line be used for prediction? Why or why not?For a given line of best fit, you compute that r = 0.5204 using n = 9 data points, and the critical value is 0.666. Can the line be used for prediction? Why or why not?For a given line of best fit, you compute that r = 0.7204 using n = 8 data points, and the critical value is = 0.707. Can the line be used for prediction? Why or why not?For a given line of best fit, you compute that r = 0 using n = 100 data points. Can the line be used for prediction? Why or why not?Data are collected on the relationship between the number of hours per week practicing a musical instrument and scores on a math test. The line of best fit is as follows: y=72.5+2.8x What would you predict the score on a math test would be for a student who practices a musical instrument for five hours a week?Identify the potential outlier in the scatter plot. The standard deviation of the residuals or errors is approximately 8.6. Figure 12.19The data points for the graph from the third exam/final exam example are as follows: (1, 5), (2, 7), (2, 6), (3, 9), (4, 12), (4, 13), (5, 18), (6, 19), (7, 12), and (7, 21). Remove the outlier and recalculate the line of best fit. Find the value of y when x = 10.The following table shows economic development measured in per capita income PCINC. Year PCINC Year PCINC 1870 340 1920 1050 1880 499 1930 1170 1890 592 1940 1364 1900 757 1950 1836 1910 927 1960 2132 Table 12.7 a. What are the independent and dependent variables? b. Draw a scatter plot. c. Use regression to find the line of best fit and the correlation coefficient. d. Interpret the significance of the correlation coefficient. e. Is there a linear relationship between the variables? f. Find the coefficient of determination and interpret it. g. What is the slope of the regression equation? What does it mean? h. Use the line of best fit to estimate PCINC for 1900, for 2000. i. Determine if there are any outliers.Linear Equations Use the following information to answer the next three exercises. A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of $25 and another fee of $12.50 an hour. What are the dependent and independent variables?Linear Equations Use the following information to answer the next three exercises. A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of $25 and another fee of $12.50 an hour. Find the equation that expresses the total fee in terms of the number of hours the equipment is rented.Linear Equations Use the following information to answer the next three exercises. A vacation resort rents SCUBA equipment to certified divers. The resort charges an up-front fee of $25 and another fee of $12.50 an hour. Graph the equation from Exercise 12.2.Use the following information to answer the next two exercises. A credit card company charges $10 when a payment is late, and $5 a day each day the payment remains unpaid. Find the equation that expresses the total fee in terms of the number of days the payment is late.Use the following information to answer the next two exercises. A credit card company charges $10 when a payment is late, and $5 a day each day the payment remains unpaid. Graph the equation from Exercise 12.4.Is the equation y=10+5x3x2 linear? Why or why not?Which of the following equations are linear? a. y=6x+8 b. y+7=3x c. yx=8x2 d. 4y=8Does the graph show a linear equation? Why or why not? Figure 12.25 Table 12.12 contains real data for the first two decades of flu reporting. Year # flu cases diagnosed # flu deaths Pre-1981 91 29 1981 319 121 1982 1,170 453 1983 3,076 1,482 1984 6,240 3,466 1985 11,776 6,878 1986 19,032 11,987 1987 28,564 16,162 1988 35,447 20,868 1989 42,674 27,591 1990 48,634 31,335 1991 59,660 36,560 1992 78,530 41,055 1993 78,834 44,730 1994 71,874 49,095 1995 68,505 49,456 1996 59,347 38,510 1997 47,149 20,736 1998 38,393 19,005 1999 25,174 18,454 2000 25,522 17,347 2001 25,643 17,402 2002 26,464 16,371 Total 802,118 489,093 Table 12.12 Adults and Adolescents only, United StatesUse the columns "year" and "# flu cases diagnosed. Why is “year” the independent variable and “# flu cases diagnosed.” the dependent variable (instead of the reverse)?Use the following information to answer the next two exercises. A specialty cleaning company charges an equipment fee and an hourly labor fee. A linear equation that expresses the total amount of the fee the company charges for each session is y=50+100x. What are the independent and dependent variables?Use the following information to answer the next two exercises. A specialty cleaning company charges an equipment fee and an hourly labor fee. A linear equation that expresses the total amount of the fee the company charges for each session is y=50+100x. What is the y-intercept and what is the slope? Interpret them using complete sentences.Use the following information to answer the next three questions. Due to erosion, a river shoreline is losing several thousand pounds of soil each year. A linear equation that expresses the total amount of soil lost per year is y = 12,000x. What are the independent and dependent variables?Use the following information to answer the next three questions. Due to erosion, a river shoreline is losing several thousand pounds of soil each year. A linear equation that expresses the total amount of soil lost per year is y = 12,000x How many pounds of soil does the shoreline lose in a year?Use the following information to answer the next three questions. Due to erosion, a river shoreline is losing several thousand pounds of soil each year. A linear equation that expresses the total amount of soil lost per year is y = 12,000x What is the y-intercept? Interpret its meaning.Use the following information to answer the next two exercises. The price of a single issue of stock can fluctuate throughout the day. A linear equation that represents the price of stock for Shipment Express is y=151.5xwhere x is the number of hours passed in an eight-hour day of trading. What are the slope and y-intercept? Interpret their meaning.Use the following information to answer the next two exercises. The price of a single issue of stock can fluctuate throughout the day. A linear equation that represents the price of stock for Shipment Express is where x is the number of hours passed in an eight-hour day of trading. If you owned this stock, would you want a positive or negative slope? Why?Does the scatter plot appear linear? Strong or weak? Positive or negative Figure 12.26Does the scatter plot appear linear? Strong or weak? Positive or negative? Figure 12.27Does the scatter plot appear linear? Strong or weak? Positive or negative? Figure 12.28The Regression Equation Use the following information to answer the next five exercises. A random sample of ten professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars). x y x y 0 2 5 12 3 8 4 9 2 7 3 9 1 3 0 3 5 13 4 10 Table 12.13 Draw a scatter plot of the data.The Regression Equation Use the following information to answer the next five exercises. A random sample of ten professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars). x y x y 0 2 5 12 3 8 4 9 2 7 3 9 1 3 0 3 5 13 4 10 Table 12.13 Use regression to find the equation for the line of best fit.The Regression Equation Use the following information to answer the next five exercises. A random sample of ten professional athletes produced the following data where x is the number of endorsements the player has and y is the amount of money made (in millions of dollars). x y x y 0 2 5 12 3 8 4 9 2 7 3 9 1 3 0 3 5 13 4 10 Table 12.13 Draw the line of best fit on the scatter plot.