Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means . Which of the following best describes the sampling distribution of the sample mean difference ?
A) It is normally distributed.
B) It is approximately normal.
C) It is student t-distributed with 88 degrees of freedom.
D) It is student t-distributed with 90 degrees of freedom.

Question

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means  . Which of the following best describes the sampling distribution of the sample mean difference  ?
A) It is normally distributed. 
B) It is approximately normal. 
C) It is student t-distributed with 88 degrees of freedom. 
D) It is student t-distributed with 90 degrees of freedom.

Quizplus · Accepted Answer

The central limit theorem states that the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (typically n > 30). In this case, both sample sizes are greater than 30, so we can assume that the sampling distribution of the sample mean difference will be approximately normal. Therefore, the best choice is B.

Two Independent Samples of Sizes 40 and 50 Are Randomly