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,andWilliam; the first names of the women are RoseandFrances. Suppose that the specified attribute is "male" and the population proportion is 0.6. Complete parts (a) through (d) below.

1. The first column of the table to the right provides the possible samples of size 3, where each person is represented by the first letter of his or her name; the second column gives the number of successesthe number of males obtainedfor

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

2. Construct a dotplot for the sampling distribution of the proportion for samples of size 3. Mark the position of the population proportion on the dotplot. Choose the correct graph below.

3. Use the third column of the table to obtain the mean of the variable

The mean is =

4. Compare the answer from part (c) to the given population proportion. Choose the correct answer below.

A.

The answers are not the same. This is because the population proportion, p, is based on the population distribution, whereas the mean of the variable p is based on the sample distribution.

B.

The answers are the same. This is because for samples of 10 or greater, the mean of the variable p will be equal to the population proportion, p.

C.

The answers are not the same. This is because the population proportion, p, is based on a larger data set, which makes it unlikely to be the same as the mean of the variable p.

D.

The answers are the same. This is because for samples of size n, the mean of the variable p equals the population proportion, p.