If two populations are not known to be normally distributed, the sampling distribution of the sample mean difference, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ , will be:
A)normally distributed only if both population sizes are greater than 30.
B)normally distributed.
C)normally distributed only if at least one of the sample sizes is greater than 30.
D)approximately normally distributed.

Question

Quizplus · Accepted Answer

According to the Central Limit Theorem, if the sample sizes are large enough (typically n > 30), the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. This applies to the difference between two sample means as well.

If Two Populations Are Not Known to Be Normally Distributed Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​

If Two Populations Are Not Known to Be Normally Distributed $\bar { X } _ { 1 } - \bar { X } _ { 2 }$