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).
1. Which of the statements gives the correct outcome of the researcher's test of the claim?
A) Because the confidence interval includes zero, the researcher can conclude the proportion of men and women who exercise regularly is the same.
B) Because the confidence interval includes zero, the researcher can conclude the proportion of men and women who exercise regularly may be the same.
C) Because the confidence interval includes zero, the researcher can conclude the proportion of men and women who exercise regularly is different.
D) Because the confidence interval includes more positive than negative values, the researcher can conclude that a greater proportion of men than women exercise regularly.
E) The researcher cannot draw a conclusion about a claim without performing a significance test.

Answer 1

Answer:

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

Step-by-step explanation:

When the null value is contained in the confidence interval we tend to fail to reject the null hypothesis.

Here, the hypothesis according to scenario are

Null hypothesis: The Proportion of men and women who exercise regularly is  same i.e. p1-p2=0.

Alternative hypothesis: The proportion of men and women who exercise regularly is not the same i.e. p1-p2≠0.

The null value here is 0. As the confidence interval is (-0.154,0.138) and it contains 0, so we fail to reject the null hypothesis and conclude that the proportion of men and women who exercise regularly is the same.