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 close together because closer proportions results in a smaller standard error, which is the denominator 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 larger absolute value of the numerator 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 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.