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Solved: Performance ratings of government agencies. The
Chapter 8, Problem 32E(choose chapter or problem)
Problem 32E
Performance ratings of government agencies. The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. A research team at George Mason University evaluated the quality of the PARS for 24 government agencies (The Public Manager, Summer 2008), where evaluation scores ranged from 12 (lowest) to 60 (highest). The accompanying file contains evaluation scores for all 24 agencies for two consecutive years. (See Exercise 2.129, p. 105.) Data for a random sample of five of these agencies are shown in the accompanying table. Suppose you want to conduct a paired difference test to determine whether the true mean evaluation score of government agencies in year 2 exceeds the true mean evaluation score in year 1.
a. Explain why the data should be analyzed using a paired difference test.
b. Compute the difference between the year 2 score and the year 1 score for each sampled agency.
c. Find the mean and standard deviation of the differences, part b.
d. Use the summary statistics, part c, to find the test statistic.
e. Give the rejection region for the test using α = .10.
f. Make the appropriate conclusion in the words of the problem.
Questions & Answers
QUESTION:
Problem 32E
Performance ratings of government agencies. The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. A research team at George Mason University evaluated the quality of the PARS for 24 government agencies (The Public Manager, Summer 2008), where evaluation scores ranged from 12 (lowest) to 60 (highest). The accompanying file contains evaluation scores for all 24 agencies for two consecutive years. (See Exercise 2.129, p. 105.) Data for a random sample of five of these agencies are shown in the accompanying table. Suppose you want to conduct a paired difference test to determine whether the true mean evaluation score of government agencies in year 2 exceeds the true mean evaluation score in year 1.
a. Explain why the data should be analyzed using a paired difference test.
b. Compute the difference between the year 2 score and the year 1 score for each sampled agency.
c. Find the mean and standard deviation of the differences, part b.
d. Use the summary statistics, part c, to find the test statistic.
e. Give the rejection region for the test using α = .10.
f. Make the appropriate conclusion in the words of the problem.
ANSWER:
Solution
Step 1 of 6
a) We have to explain why the data should analyzed by using paired difference test
Here the data is collected 2 times for the same sample once in year 1 and again they collected the data for the same sample in the year 2
Here the samples are not independent, we can’t use the independent samples test
Hence we should analyze the data by using paired difference test