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, II, and III
B) I and III
C) I and II
D) III only

Question

Quizplus · Accepted Answer

Statement I is true because the pooled sample proportion estimates the common value of $p_1$ and $p_2$ under the null hypothesis of equal proportions. Statement III is true because the pooled sample proportion is calculated as the total number of successes in both samples divided by the total number of observations in both samples. Statement II is false because the pooled sample proportion is not simply the average of 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 $\bar { p }$