Concept explainers
An examination in psychology has been taken by psychology majors and also by some students from other majors. It is widely believed that the scores for both groups are
examinations completed by psychology majors and an independent random sample of
examinations completed by students from other majors are selected. Among sampled students, the psychology majors scored a mean of
points with a variance of
, and the students from other majors scored a mean of
points with a variance of
. Can we conclude, at the
significance level, that the population variance of scores of psychology majors,
, is less than
, the population variance of scores of other majors?
Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
|
Trending nowThis is a popular solution!
Step by stepSolved in 6 steps with 6 images
- An amusement park conducted an internal audit on the wait times of its customers for the park's rides during a summer weekend. The audit found that the wait times of customers for the Shooting Star ride had a population mean of 31.2 minutes with a population variance of 6.3 minutes The park's head executive has doubts about the audit's findings concerning the Shooting Star ride. He hires an inspector to check these findings. On a summer weekend, the inspector takes a sample of 12 people at random waiting in line for the Shooting Star. She records their wait times and finds that the sample mean is 33.1 minutes and the sample variance is 4.8 minutes 2 Fill in the blanks below with the proper notation for the population mean, the population variance, and the sample variance. 66°F Cloudy Population mean: (Choose one) = 31.2 minutes X Population variance: (Choose one) = 6.3 minutes 2 Sample variance: (Choose one) 2 = 4.8 minutes Continue 3 W E 5. D DIL R Q Search 5 G 7 G Y U H 8 X C V B N M…arrow_forwardThe Insurance Institute for Highway Safety publishes data on the total damage suffered by compact automobiles in a series of controlled, low-speed collisions. The cost for a sample of 9 cars, in hundreds of dollars, is provided below. 10, 6, 8, 10, 5, 3.5, 7.5, 7,9.5 Find interquartile range for mileage data and value of variance.arrow_forwardA psychology graduate student wants to test the claim that there is a significant difference between the IQs of spouses. To test this claim, she measures the IQs of 9 married couples using a standard IQ test. The results of the IQ tests are listed in the following table. Using a 0.10 level of significance, test the claim that there is a significant difference between the IQs assuming that the population distribution of the paired differences is approximately normal. Let the spouse 1 group be Population 1 and let the spouse 2 group be Population 2. Spouse 1 Spouse 2 IQs of Married Couples 124 113 97 123 121 101 128 116 96 126 119 100 Copy Data Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places. 124 111 127 113 107 111arrow_forward
- A union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, u, of foodservice workers in the U.S. Last year's mean hourly wage was $8.25, and there is reason to believe that this year's value is less than last year's. The union decides to do a statistical test to see if the value has indeed decreased. The union chooses a random sample of this year's wages, computes the mean of the sample to be $7.98, and computes the standard deviation of the sample to be $1.25. Based on this information, answer the questions below. What are the null hypothesis (H) and the alternative hypothesis (H,) that should be used for the test? |Ho: u is ? H: u is ? v|? ? In the context of this test, what is a Type I error? v the hypothesis that u is ? A Type I error is ? fact, u is ? v when, in Suppose that the union decides not to reject the null hypothesis. What sort of error might it be making? ?arrow_forwardA union of restaurant and foodservice workers would like to estimate this year's mean hourly wage, u, of foodservice workers in the U.S. Last year's mean hourly wage was $8.08, and there is reason to believe that this year's value is different from last year's. The union decides to do a statistical test to see if the value has indeed changed. The union chooses a random sample of this year's wages, computes the mean of the sample to be $8.48, and computes the standard deviation of the sample to be $1.25. Based on this information, answer the questions below. What are the null hypothesis (H) and the alternative hypothesis (H,) that should be used for the test? H: u is [? |H: u is ? ? In the context of this test, what is a Type II error? A Type II error is ? v the hypothesis that u is ? when, in fact, u is ? Suppose that the union decides to reject the null hypothesis. What sort of error might it be making? ?arrow_forwardA large company that produces allergy medications claims that Americans lose an average of 40 hours of work to problems related to seasonal allergies. A consumer advocacy group believes that company's claim exhibits self-interest bias. In other words, the advocacy group believes that the actual mean number of missed hours is less than claimed. The advocacy group would like to obtain statistical evidence about this issue and takes a random sample of 100 American workers. They find that these 100 people lost and average of 38 hours due to seasonal allergy symptoms. The standard deviation is 9.5 hours. (c) Based on your selection from part (b), what is the value of the standardized test statistic for this significance test? (d) Based on your selection from part (b), what is the P-value for this significance test? (e) What is the correct decision for this test, using a 0.05 level of signifcance? A) Reject the null hypothesis B) Do not reject the null…arrow_forward
- Use the following information to answer the question. A researcher wants to study different messaging platforms by collecting data on 40 individuals. Half of the individuals only use iMessage while the other half only use What's App. For the individuals who only used iMessage, they sent an average of 280 messages with a sample variance of 170 in the past week. For the individuals who only used What's App, they sent an average of 295 messages with a sample variance of 182 in the past week. Determine if there is a significant difference between the average messages sent between the two groups of individuals. Use a significance level of 1%. What is the null hypothesis? Group of answer choices A. The iMessage group on average sent more messages than the What's App group. B. The iMessage group on average sent less messages than the What's App group. C. There is no difference in the average number of messages sent between the two groups. D. There is a difference in the average…arrow_forwardA school psychologist is interested in whether or not teachers affect the anxiety scores among students taking the Statistics exam. The data below are the standardized anxiety test scores for students with the three different teachers. Teacher’s Name Ms. San Pedro Ms. San Juan Ms. San Jose 8 23 22 10 14 18 12 12 14 11 8 22 13 15 22 15 16 10 16 14 11 17 19 9 9 10 10 13 Perform an analysis of variance at the 0.05 level of significance.arrow_forwardIn college, talented runners may join a cross-country team. Runners tend to run their best times when they run even splits. Even splits occur when the runners maintain an even pace throughout the race. The cross-country coach wants to estimate the typical variability in his best runner's 1-mile splits. He takes a random sample of 25 of this runner's mile splits and finds that this runner's mean 1-mile split is 5.44 minutes per mile, with a standard deviation of 0.14 minutes per mile. This runner's 1-mile splits follow a normal distribution. (a) Find the chi-square critical values XL² and Xu² to be used in constructing a 95% confidence interval for the true population standard deviation. (Round your answers to two decimal places.) XL²= XU²= (b) Find the 95% confidence interval for the true variability in his best runner's 1-mile splits. (Round your answers to three decimal places.) lower bound and the upper boundarrow_forward
- Two surfers and statistics students collected data on the number of days on which surfers surfed in the last month for 30 longboard (L) users and 30 shortboard (S) users. Treat these data as though they were from two independent random samples. Test the hypothesis that the mean days surfed for all longboarders is larger than the mean days surfed for all shortboarders (because longboards can go out in many different surfing conditions). Use a level of significance of 0.05. Longboard: 4,10,9,4,9,8,8,6,7,9,11,11,9,15,11,16,13,11,12,18,18,13,12,15,20,22,7,24,22,24 Shortboard: 6,4,4,6,9,9,6,8,4,8,8,5,9,9,4,16,12,9,13,13,10,13,11,12,14,14,9,21,19,10 Determine the hypotheses for this test. Choose the correct answer below. C. Ho: HL Hs Hai HL # Hs Ha: HL = Hs O D. Ho: HL = Hs Ha: HL Hs F. Ho: HL # Hs Ha: HL = Hs Find the test statistic for this test. t%=D (Round to two decimal places as needed.) Find the p-value for this test. p-value = (Round to three decimal places as needed.) What is the…arrow_forwardIn the US, 45.9% of all people have type O blood, 39.7% have type A blood, 11.2% have type B blood and 3.2% have type AB blood. A researcher wants to see if the distribution of blood type is different for millionaires. The table below shows the results of a random sample of 569 millionaires. What can be concluded at the significant level of a = 0.01. The test-statistic for this data = The p-value for this sample =arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman