If two random samples of sizes $n _ { 1 }$ and $n _ { 2 }$ 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 $n _ { 1 }$ and $n _ { 2 }$ are both larger than 30.
D)approximately normal regardless of $n _ { 1 }$ and $n _ { 2 }$ .

Question

Quizplus · Accepted Answer

According to the Central Limit Theorem, the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (usually $n > 30$). This applies even if the populations from which the samples are drawn are not normally distributed. Therefore, the sampling distribution of the difference between two sample means, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$, will also be approximately normal if both $n _ { 1 }$ and $n _ { 2 }$ are larger than 30.

If Two Random Samples of Sizes n1n _ { 1 }n1​

If Two Random Samples of Sizes $n _ { 1 }$