Question

In a paired​ t-test, when will the distribution of sample means of the differences be normal or approximately​ normal?

Select all that apply.

A.

When the sample is representative of the population of interest

B.

When the sample size is at least 30

C.

When the distribution of differences in the population is normal

D.

When all of the above are true

Answer 1

In a paired​ t-test, the distribution of sample means of the differences be normal or approximately​ normal when -

ans-> D) When all of the above are true

Since, sample should always be representative of the population of interest for testing purpose, if the distribution of differences in the population is normal, the distribution of sample means of the differences will also be normal.

When the sample size is at least 30, even if the distribution of differences in the population is not normal,  the distribution of sample means of the differences will be approximately normal, using central limit theorem.