I was thinking about the next problem: Test A and Test B use the same sample, the same test, to test the same simple hypotheses. Test A has a greater power than Test B. So if a researcher rejects H0 in test B, he is sure to reject H0 in test A. YES/NO
I do not understand why the answer is NO. If Test A has a greater power than Test B, and they perform the same test on the same sample, why does it not necessarily mean that the rejection area of Test A contains the rejection area of Test B?
Thanks!!