Chapter 8.3, Problem 8.32ACB

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 2.131, p. 108.) 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.

Agency	Year 1 Score	Year 2 Score
GSA	34	40
Agriculture	33	35
Social Security	33	33
USAID	32	42
Defense	17	32

1. a. Explain why the data should be analyzed using a paired difference test.
2. b. Compute the difference between the year 2 score and the year 1 score for each sampled agency.
3. c. Find the mean and standard deviation of the differences, part b.
4. d. Use the summary statistics, part c, to find the test statistic.
5. e. Give the rejection region for the test using α = .10.
6. f. Make the appropriate conclusion in the words of the problem.