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 $p _ { 1 }$ and $p _ { 2 }$ under the assumption of equal proportions.
II. It is obtained by averaging the two sample proportions $\hat { p } _ { 1 }$ 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

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 $p _ { 1 }$ and $p _ { 2 }$ under the assumption of equal proportions.
II. It is obtained by averaging the two sample proportions $\hat { p } _ { 1 }$ 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

Quizplus · Accepted Answer

The pooled sample proportion estimates the common value of $p_1$ and $p_2$ under the assumption of equal proportions and is equal to the proportion of successes in both samples combined. It is not obtained by simply averaging the two sample proportions.

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

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