Question

When comparing two sample proportions with a​ two-sided alternative​ hypothesis, all other factors being​ equal, will you get a smaller​ p-value if the sample proportions are close together or if they are far​ apart? Explain. Choose the correct answer below.

A. The​ p-value will be smaller if the sample proportions are far apart because a larger difference results in a larger absolute value of the numerator of the test statistic.

B. The​ p-value will be smaller if the sample proportions are far apart because a larger difference results in a pooled proportion closer to​ 0.5, and a pooled proportion close to 0.5 results in a smaller standard​ error, which is the denominator of the test statistic.

C. The​ p-value will be smaller if the sample proportions are close together because the difference between them is smaller.

D. The​ p-value will be smaller if the sample proportions are close together because closer proportions results in a smaller standard​ error, which is the denominator of the test statistic.

Answer 1

CORRECT ANSWER IS:

A. The​ p-value will be smaller if the sample proportions are far apart because a larger difference results in a larger absolute value of the numerator of the test statistic.

The z-statistic is computed as follows:

i.e. Z statistic is directly proportional to the difference of the two sample proportions.

This means the more the sample proportions are apart, the higher will be the value of the z statistic and consequently the smaller will be the p-value,

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