# Question: This exercise involves the use of an unrealistically small population

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.

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?

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.

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?

**View Solution:**## Answer to relevant Questions

x = 40, n = 50, 95% level. a. Use the one-proportion plus-four z-interval procedure, as discussed on page 449, to find the required confidence interval. b. Compare your result with the corresponding confidence interval ...In the May 2008 New York Times article “More Mothers Breast-Feed, in First Months at Least,” G. Harris reported that 77% of new mothers breast-feed their infants at least briefly, the highest rate seen in the United ...x = 40, n = 50, H0: p = 0.6, H0: p > 0.6, α = 0.01 a. Determine the sample proportion. b. Decide whether using the one-proportion z-test is appropriate. c. If appropriate, use the one-proportion z-test to perform the ...Repeat parts (b)–(e) of Exercise 11.5 for samples of size 3. (There are 10 possible samples.) Industry Research polled teenagers on sunscreen us e. The survey revealed that 46% of teenage girls and 30% of teenage boys regularly use sunscreen before going out in the sun. a. Identify the specified attribute. b. ...Post your question