8.32 Performance ratings of government agencies. The U.S. Office of Management and Budget (OMB) requires govern- mas ment agencies to produce annual performance and account- ing 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 (high- est). The accompanying le contains evaluation scores for all 24 agencies for two consecutive years (See Exercise 2.131, p. 108.) Data for a random sample of ve 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 Source: J. Ellig and H. Wray, \"Measuring Performance Reporting Quality." The Public Manager, Vol. 3?. No. 2. Summer 2008 (p. 66}. Copyright 2008 by Jerry Ellig. Used by permission of Jerry Ellig. a. Explain why the data should be analyzed using a paired difference test. I). 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 differ- ences, part b. I]. Use the sunnnary statistics, part c, to nd the test statistic. e. Give the rejection region for the test using a: = .10. f. Make the appropriate conclusion in the words of the