In testing the difference between two means from two normally distributed independent populations,the distribution of the difference in sample means will be:
A)Normally distributed only if sample sizes are equal.
B)Normally distributed only if both population standard deviations are known.
C)Normally distributed.
D)Normally distributed if both sample sizes are very large.
E)Normally distributed only if both population variances are equal.

Question

Quizplus · Accepted Answer

The distribution of the difference in sample means will be normally distributed regardless of sample size, population standard deviation, or population variance if the two populations are normally distributed and the samples are independent. This is known as the Central Limit Theorem for difference in sample means. Therefore, option C is the best choice.

In Testing the Difference Between Two Means from Two Normally