The sampling distribution of $\bar { x } _ { 1 } - \bar { x } _ { 2 }$ is normal if the sampled populations are normal, and approximately normal if the populations are nonnormal and the sample sizes n₁ and n₂ are large.

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the difference between two sample means is approximately normal if the sample sizes are large, regardless of the population distribution. If the populations are normal, the sampling distribution is exactly normal.

The Sampling Distribution Of xˉ1−xˉ2\bar { x } _ { 1 } - \bar { x } _ { 2 }xˉ1​−xˉ2​

The Sampling Distribution Of $\bar { x } _ { 1 } - \bar { x } _ { 2 }$