In the context of a hypothesis test for two proportions, which of the following statements about the pooled sample proportion, $\bar { p }$ is/are true?
I. It estimates the common value of $p _ { 1 } \text { and } p _ { 2 }$ under the assumption of equal proportions.
II. It is obtained by averaging the two sample proportions $\hat { p } _ { 1 } \text { and } \hat { p } _ { 2 }$
III. It is equal to the proportion of successes in both samples combined.
A) I and II
B) III only
C) I, II, and III
D) I and III

Question

Quizplus · Accepted Answer

The pooled sample proportion, $\bar { p }$, is used under the assumption that the two populations have the same proportion (statement I is true). It is calculated by combining the successes and the total number of trials from both samples, effectively finding the proportion of successes in both samples combined (statement III is true). It is not simply an average of the two sample proportions (statement II is false), which makes option D correct.

In the Context of a Hypothesis Test for Two Proportions pˉ\bar { p }pˉ​

In the Context of a Hypothesis Test for Two Proportions $\bar { p }$