Five salespeople report these monthly sales amounts (given in thousands of dollars):

a. Calculate the mean sales for each salesperson and the variances of each salesperson’s sales amounts. At the 5% significance level, does either the Hartley test or the Cochran test of homogeneity of variance convince us that the variances are unequal?

b. Perform the Bartlett test of homogeneity of variance on the five sample sales amounts. Use the 5% significance level.

c. What is the relevance of tests of homogeneity of variance to analysis of variance?

d. Perform a one-way analysis of variance to determine if it can be concluded at the 5% significance level that mean sales amounts differ among the five salespeople.

e. Use the Scheffé test to determine which pairs of treatment group means are different at the 5% significance level.

f. Apply the Tukey test at the 5% significance level for the differences between the means of groups 3 and 5, and 4 and 5. What hypotheses are being tested, and what conclusions are reached?