A sales analyst wants to determine whether there is a difference in the mean monthly sales of a company's four sales regions. Several salespersons from each region are randomly selected and they provide their sales amounts (in thousands of dollars) for the previous month. The results are shown in the table. At a = 0.05, can the analyst conclude that there is a difference in the mean monthly sales among the sales regions? Assume that each population of sales is normally distributed and that the population variances are equal.
|
North
|
East
|
South
|
West
|
|
34
|
47
|
40
|
21
|
|
28
|
36
|
30
|
30
|
|
18
|
30
|
41
|
24
|
|
24
|
38
|
29
|
37
|
|
44
|
|
23
|
a. Identify the claim and state H0 and Ha.
b. Identify the level of significance a.
c. Determine the degrees of freedom for the numerator and the denominator.
d. Find the critical value F0 and identify the rejection region.
e. Find the test statistic F. Sketch a graph.
f. Decide whether to reject the null hypothesis.
g. Interpret the decision in the context of the original claim.