The executives at a national retailer wish to examine whether there is any significant difference in the mean sales performance across its branch offices. Monthly sales totals (in dollars) were collected for 31 randomly selected sales representatives from each of four branch offices (Coastal, Lakeside, Gulfview, Rockies). The sample data can be found in the data file "Sales."

(a) Construct and conduct an appropriate hypothesis test to determine whether mean sales values differ across the four branch offices. Use a 5% level of significance. Interpret your conclusion within the context of this problem.

(b) The executives would like to promote one manager of the branch office with the highest mean sales. Can you identify this office? If so, provide statistical reasoning and explain your answer. If not, explain why not.

(c) The executives would like to demote one manager of the branch office with the lowest mean sales. Can you identify this office? If so, provide statistical reasoning and explain your answer. If not, explain why not.

(d) Are yourconclusions in (b) and (c) robust to a change in the assumptions, namely that the populations do not have equal variances? How do you know? Explain completely.