Question

Question: 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. 132.) 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.

Source: J. Ellig and H. Wray, “Measuring Performance Reporting Quality,” The Public Manager, Vol. 37, No. 2, Summer 2008 (p. 66). Copyright © 2008 by Jerry Ellig. Used by permission of Jerry Ellig.

a. Explain why the data should be analyzedusing 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. Use the summary statistics, part c, to find the test statistic.

e. Give the rejection region for the test using a = .10.

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

Short answer

1. The paired t-test is a technique for determining whether or not the mean difference between two values is zero. Since the two samples contain similar individuals, their names indicate that they are paired and reliant.

2. Year 1 and year 2 score is (-6, -2,0, -10, -15)

3. 6.0663

4. -2.43279

5. 4

6. The mean genuine evaluation score in the first year.

Step-by-step solution

(a) Paired t-test

When we are concerned with the contrast among two variables for similar participants as well as data obtained from the identical pair of organizations, we utilize the paired - t-test.

(b) Difference between Year 2 and Year 1 score

(c) Mean of the difference

(d) Use test statistics

Null Hypothesis: µ_d = 0

Alternative Hypothesis: µ_d < 0

(e) Rejection region for the test

(f) Conclusion

With the t-score, ( -2.43279 ) < - 1.533 we can reject the null hypothesis at 0. I significance level as well as conclude that there is enough proof to demonstrate that the accurate mean score of evaluation authority agencies in 2008 exceeds the mean genuine evaluation score in 2007