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:
A) normally distributed
B) approximately normal
C) t - distributed with 98 degrees of freedom
D) chi-squared distributed with 99 degrees of freedom

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:
A) normally distributed 
B) approximately normal 
C) t - distributed with 98 degrees of freedom 
D) chi-squared distributed with 99 degrees of freedom

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