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A study identified top accounting firms across the United States. The Southeast and Gulf Coast regions reported the highest combined growths. A characteristic description of the accounting firms in the Southeast and Gulf Coast regions included the number of partners in the firm. Below represents the number of partners within various firms of the two regions [Southeast and Gulf Coast].
Southeast 174 Gulf Coast 79
Southeast 45 Gulf Coast 106
Southeast 29 Gulf Coast 22
Southeast 51 Gulf Coast 22
Southeast 40 Gulf Coast 38
Southeast 10 Gulf Coast 17
Southeast 29 Gulf Coast 27
Southeast 37 Gulf Coast 21
Southeast 32 Gulf Coast 17
Southeast 22 Gulf Coast 12
Southeast 9 Gulf Coast 9
Southeast 30 Gulf Coast 6
Southeast 21 Gulf Coast 9
Gulf Coast 12
Gulf Coast 18
(a) At the 0.05 level of significance, is there evidence of a difference in the variability in numbers of partners for Southeast region accounting firms and Gulf Coast accounting firms? (Include: null and alternate hypotheses, value of test statistic, decision rule, conclusion in a complete sentence that includes why in terms of the decision rule.)
(b) Interpret the p-value.
(c) What assumption do you have to make about the two populations in order to justify the use of the F test?
(d) Based on (a) and (b), which t test [Pooled Variance t-test or Separate Variance t-Test] should you use to test whether there is a significant difference in the
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