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

Question

Quizplus · Accepted Answer

The pooled sample proportion estimates the common value of $ p_1 $ and $ p_2 $ under the null hypothesis of equal proportions and is calculated as the proportion of successes in both samples combined, not by averaging the two sample proportions.

In the Context of a Hypothesis Test for Two Proportions p‾\overline { \mathrm { p } }p​

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