A pool of six candidates for three managerial positions includes three females and three males. Table 7.31 shows the results.

(a) Denote the three females by F1, F2, and F3 and the 3 males by M1, M2, and M3. Identify the 20 distinct samples of size three that can be chosen from these six individuals.

(b) Let πˆ 1 denote the sample proportion ofmales selected and πˆ 2 the sample proportion of females. For Table 7.28,

πˆ 1 − πˆ 2 = (2/3) − (1/3) = 1/3. Of the 20 possible samples, show that 10 have πˆ 1 − πˆ 2 ≥ 1/3. Thus, if the three managers were randomly selected, the probability would equal 10/20 = 0.50 of obtaining πˆ 1 −πˆ 2 ≥ 1/3. This is the TABLE 7.31 Chosen for Position Gender Yes No Male 2 1 Female 1 2 reasoning that provides the one-sided P-value for Fisher’s exact test.

(c) Find the P-value if all three selected are male.

Interpret.