Refer to The Public Manager (Summer 2008) performance ratings of government agencies, Exercise 8.32. Evaluation scores for all agencies were obtained for two consecutive years and are saved in the file. Data for a random sample of five of these agencies are shown in the table below. Suppose you want to determine whether the distribution of evaluation scores in year 2 is shifted above the distribution of evaluation scores in year 1.

a. Specify the null and alternative hypotheses for a Wilcoxon signed rank test of the data.

b. In Exercise 8.32b you computed the difference between the two scores for each sampled agency. Now rank the absolute values of these differences.

c. Sum the ranks of the positive differences, part b. Also, sum the ranks of the negative differences.

d. Use the results, part c, to find the test statistic.

e. Give the rejection region for the test using α = .05.

f. Make the appropriate conclusion in the words of the problem.

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Year 1 Score Year 2 Score Agency 34 33 40 40 35 GSA Agriculture HHS 35 42 32 37 32 USAID Defense 17