7.57. A pool ofsix candidates for three managerial positions includes three females and three males. Table 7.26 shows the results.

(a) Denote the three females by F\, F2, E3 and the three males by M\, M2. M3. Identify the 20 distinct samples of size three that can be chosen from these six individuals.

(b) Let Tr\ denote the sample proportion of males selected and 77-2 the sample proportion of females. For Table 7.26, tti — tt2 =

(2/3) — (1/3) = 1/3. Ofthe 20 possible samples, show that 10 have 771 _ 7T2 — 1/3. Thus, if the three managers were randomly selected, the probability would equal 10/20 = 0.50 of obtaining 771 — 772 — 1/3. In fact, this is the reasoning that provides the one-sided P-valuc for Fisher's exact test.

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

Interpret.

TABLE 7.26 Chosen for Position Gender Yes No Male 2 1 Female 1 2