3.39 Of six candidates for three managerial positions, denote the females by F1, F2, F3 and the males by M1, M2, M3.

a. Identify the 20 possible combinations of candidates that could be selected. Con-

struct the contingency table for the actual sample, which is (F2, M1, M3).

b. Let p₁ denote the sample proportion of males selected and p₂ the sam-

ple proportion of females selected. Of the 20 possible samples, show that 10 have pi P2≥3. Thus, if the three managers were randomly selected, P (p1 - P2 ≥ 3) = 10/20 = 0.50. Explain why this is the P-value for Fisher's exact test with Ηα: πι > π2.