If two samples are selected independently from two non-normal populations, then the sampling distribution of $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is only approximately normal provided that either n₁ or n₂ is 30 or more.

Question

Quizplus · Accepted Answer

The sampling distribution of $\bar{X}_1 - \bar{X}_2$ is approximately normal if both sample sizes $n_1$ and $n_2$ are 30 or more, not just one. This is due to the Central Limit Theorem, which requires large sample sizes for both samples to ensure normality.

If Two Samples Are Selected Independently from Two Non-Normal Populations Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​

If Two Samples Are Selected Independently from Two Non-Normal Populations $\bar { X } _ { 1 } - \bar { X } _ { 2 }$