Question

a. Explain to someone how you know that if the results of a hypothesis test are significant at the 1% level, the result MUST be significant at the 5% level.

b. Explain to someone how you know that if the results of a hypothesis test are significant at the 5% level, you don’t know if the results are significant at the 1% level.

Answer 1

(a) Since level of significance , or , is the maximum probability of rejecting true null hypothesis. If this maximum probability is 0.01(i.e. 1% level) to reject the true null hypothesis then at probability value 0.05 ( 5% level) the null hypothesis must be rejected.

(b) Similarly , if maximum probability to rejecting true null hypothesis is 0.05 (5% level) ,then we don't known that results are significant at the probability value 0.01(1% level).