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. O A. 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. O B. 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. OC. The p-value will be smaller if the sample proportions are close together because the difference between them is smaller. O D. The p-value will be smaller if the sample proportions are far apart because larger difference results in a larger absolute value of the numerator of the test statistic.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.4: Collecting Data
Problem 3E
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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 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.
B. 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.
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 larger absolute value of the numerator of the test statistic.
O O O
Transcribed Image Text: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 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. B. 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. 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 larger absolute value of the numerator of the test statistic. O O O
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