The sampling distribution of $\bar { p } _ { 1 }$

Question

The sampling distribution of $\bar { p } _ { 1 }$ - $\bar { p } _ { 2 }$ is approximated by a normal distribution if _____ are all greater than or equal to 5. A) n₁p₂, p₂(1 - n₂), n₂p₁, p₁(1 - n₁) B) n₁p₁, p₁(1 - n₁), n₂p₂, p₂(1 - n₂) C) n₁p₂, n₁(1 - p₂), n₂p₁, n₂(1 - p₁) D) n₁p₁, n₁(1 - p₁), n₂p₂, n₂(1 - p₂)

Quizplus · Accepted Answer

The sampling distribution of the difference between two sample proportions $\bar{p}_1 - \bar{p}_2$ is approximately normal if the sample sizes are large enough. Specifically, the conditions $n_1p_1$, $n_1(1-p_1)$, $n_2p_2$, and $n_2(1-p_2)$ should all be greater than or equal to 5.

The Sampling Distribution Of pˉ1\bar { p } _ { 1 }pˉ​1​