Suppose that we perform a hypothesis testing at 2 level of s

Suppose that we perform a hypothesis testing at 2% level of significance. For which p-value of the following do we NOT reject the null hypothesis?

A) p-value= 0.001

B) p-value= 0.005

C) p-value= 0.01

D) p-value= 0.05

The answer is D, but I\'m not too sure how to answer this. There is also a similar question with the same answer choice that is asking if we do a hypothesis test at 0.1% , which value would we REJECT the null hypothesis (Answer is A,p-value=0.001).Thank you for your help!

Solution

we do not reject null if p-value > alpha, ie. if p-value is > 0.02, which is the case in option (D)

We reject if p-value <= alpha, that is why in second question we reject when p-value = 0.001 = alpha = 0.001