Public defenders’ salaries. Random samples of seven lawyers employed as public defenders were selected from each of three major cities. Their salaries are recorded in the accompanying table. You have been hired to determine whether differences exist among the salary distributions for public defenders in the three cities. Atlanta Los Angeles Washington, D.C. $39,600 $47,400 $48,000 89,900 140,000 86,900 66,700 68,000 58,000 43,900 48,700 82,600 82,200 74,400 83,200 88,600 102,000 61,800 64,800 54,500 65,000 Source: Based on average salaries reported in www.glassdoor.com.

a. Under what circumstances would it be appropriate to use the F-test for a completely randomized design to perform the required analysis?

b. Which assumptions required by the F-test are likely to be violated in this problem? Explain.

c. Specify the null hypothesis for a Kruskal-Wallis test.

d. Rank the 21 measurements in the data set.

e. Find the rank sums and calculate the test statistic.

f. Give the rejection region for the test at a = .05. g. Is there sufficient evident to conclude that the salary distributions for the three cities differ?