In testing the difference between two population means using two independent samples, the sampling distribution of the sample mean difference x?1 ? x?2 is normal if the A. populations are normal.
B. population sizes are both greater than 30.
C. populations are nonnormal and the sample sizes are large.
D. sizes are both greater than 30.

C. populations are non normal and the sample sizes are large.

Step-by-step explanation:

To test hypotheses about the difference between two populations means we deal with the following three cases.

1) both the populations are normal with known standard deviations.

2)both the populations are normal with unknown standard deviations.

3) both the populations are non normal in which case both the  sample sizes are necessarily large.

So option C is the correct answer.

irrational, cannot