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 text $p _ { 1 }$ and $p _ { 2 }$ under the assumption of equal proportions.
II. It is obtained by averaging the two sample proportions $\hat { p }$ 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 text $p _ { 1 }$ and $p _ { 2 }$ under the assumption of equal proportions.
II. It is obtained by averaging the two sample proportions $\hat { p }$ 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 is used under the assumption that the two populations have the same proportion (I), and it is calculated by combining the successes and the total number of trials from both samples to get the overall proportion (III). It is not simply an average of the two sample proportions (II).

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

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