If two random samples of sizes n₁ and n₂ are selected independently from two non-normally distributed populations,then the sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ ,is A) always non-normal B) always normal C) approximately normal only if n₁ and n₂ are both larger than or equal to 30 D) approximately normal regardless of n₁ and n₂

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$, is approximately normal only if the sample sizes from both populations are larger than or equal to 30, regardless of the distribution of the populations. This is known as the Central Limit Theorem. If the sample sizes are smaller than 30, the distribution of the sample mean difference may be non-normal even if the populations are normal.

If Two Random Samples of Sizes N1 and N2 Are Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​

If Two Random Samples of Sizes N₁ and N₂ Are $\bar { X } _ { 1 } - \bar { X } _ { 2 }$