51. A pool of six candidates for three managenal positions includes three feinales and three males Table 7.20 shows the results.

a) Denote the three females by F, F. F 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

f, denote the sample proportion of males selected and f the sample proportion of females. For Table 7.20.1-(2/3)-(1/3)=1/3. Of the 20 possible samples, show that 10 have - 2 1/3. Thus. if the three managers were randomly selected. the probability would equal 10/20.5 of obtaining 1/3 In fact, this is the 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 TABLE 7.20 Chosen for Position Gender Yes No Male 2 1 Female 1 2