Question

In a given situation, suppose H0 (null hypothesis) was not rejected at alpha= .02.

Would H0 also be retained at alpha = .01?

would H0 also be retained at alpha = .05?

I'm thinking yes and can't tell.

I agree

If you did not reject Ho at P = .02, You would definitely not reject it at the .01 level.

However, it is possible that it could still be rejected at the .05 level. You are allowing the probability of larger alpha error in that case.

I hope this helps. Thanks for asking.