Question

A researcher wants to test the claim that the proportion of men and women who exercise regularly is not the same. He finds that 42 of 65 randomly selected men and 34 of 52 randomly selected women report exercising regularly. A 90% confidence interval for the difference in population proportions is (−0.154, 0.138). Which of the statements gives the correct outcome of the researcher's test of the claim?
Because the confidence interval includes zero, the researcher can conclude the proportion of men and women who exercise regularly is the same.
Because the confidence interval includes zero, the researcher can conclude the proportion of men and women who exercise regularly may be the same.
Because the confidence interval includes zero, the researcher can conclude the proportion of men and women who exercise regularly is different.
Because the confidence interval includes more positive than negative values, the researcher can conclude that a greater proportion of men than women exercise regularly.
The researcher cannot draw a conclusion about a claim without performing a significance test.

Answer 1

Answer:

Because the confidence interval includes zero, the researcher can conclude the proportion of men and women who exercise regularly may be the same.

Explanation:

When constructing a two-proportion z-interval, it is important to look for the value zero. A value of zero in the interval shows there is no difference in the proportions between the two populations.

If the interval contains all positive numbers, it implies the true proportion for sample 1 is greater than that for sample 2. If the interval contains all negative numbers, it implies the true proportion for sample 1 is less than that for sample 2.