Two independent samples of sizes 50 and 50 are randomly selected from two populations to test the difference between the population means, . The sampling distribution of the sample mean difference is:

Question

Two independent samples of sizes 50 and 50 are randomly selected from two populations to test the difference between the population means,  . The sampling distribution of the sample mean difference  is:

Quizplus · Accepted Answer

According to the Central Limit Theorem, when sample size is sufficiently large (usually considered as n>30), the sampling distribution of the sample mean difference will be approximately normal regardless of the underlying population distribution. In this case, both samples have a size of 50, which is larger than 30, so we can assume that the sampling distribution of the sample mean difference is approximately normal.

Two Independent Samples of Sizes 50 and 50 Are Randomly