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

Multiple Choice

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