An executive at the home offi­ce of Big Rock Life Insurance is considering three branch managers as candidates for promotion to vice president. The branch reports include records showing sales volume for each salesperson in the branch (in hundreds of thousands of dollars). A random sample of these records was selected for salespersons in each branch. All three branches are located in cities in which per capita income is the same. The executive wishes to compare these samples to see if there is a signifi­cant difference in performance of salespersons in the three different branches. If so, the information will be used to determine which of the managers to promote.

Use an a = 0.01 level of signifi­cance. Shall we reject or not reject the claim that there are no differences among the performances of the salespersons in the different branches?

In the problem, please provide the following information.

(a) What is the level of signifi­cance? State the null and alternate hypotheses.

(b) Find SS_TOT, SS_BET, and SSW and check that SS_TOT – SSB_ET + SS_W. Find d.f._BET, d.f._W, MS_BET, and MS_W. Find the value of the sample test statistic F (F ratio).

What are the degrees of freedom?

(c) Find (or estimate) the P-value of the sample test statistic.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

(e) Interpret your conclusion in the context of the application.

(f) Make a summary table for your ANOVA test.

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Branch Managed by Adams 7.2 6.4 10.1 11.0 9.9 10.6 Branch Managed by McDale 8.8 10.7 11.1 9.8 Branch Managed by Vasquez 6.9 10.5 11.4