This exercise involves the use of an unrealistically small population to provide a concrete illustration for the exact distribution of a sample proportion. A population consists of three men and two women. The first names of the men are Jose, Pete, and Carlo; the first names of the women are Gail and Frances. Suppose that the specified attribute is “female.”

a. Determine the population proportion, p.

b. The first column of the following table provides the possible samples of size 2, where each person is represented by the first letter of his or her first name; the second column gives the number of successes—the number of females obtained—for each sample;

and the third column shows the sample proportion. Complete the table.

Number of females Sample proportion Sample x pˆ

J, G 1 0.5 J, P 0 0.0 J, C 0 0.0 J, F 1 0.5 G, P G, C G, F P, C P, F C, F

c. Construct a dotplot for the sampling distribution of the proportion for samples of size 2. Mark the position of the population proportion on the dotplot.

d. Use the third column of the table to obtain the mean of the variable pˆ.

e. Compare your answers from parts

(a) and (d). Why are they the same?