Question

A) If sample data are such that the null hypothesis is rejected at the alpha=5% level of significance based upon a 2 tailed test, is Ho also rejected at the alpha=1% level of significance? Explain.

B) If a 2 tailed hypothesis test leads to rejection of the null hypothesis at a certain level of significance, would the corresponding 1 tailed test lead to rejection of the null hypothesis? Explain.

Answer 1

(A) Rejection of null hypothesis at 5% significance level does not necessarily mean that the null hypothesis will also be rejected at 1% significance level.

This is because the p value must be less than 5% for rejecting null hypothesis, but this does not mean that the p value is also less than 1%

if p value is less than 1% significance level, then only we can reject the null hypothesis at 1% as well as 5% significance level

if p value is not less than 1%, but less than 5% significance level, then we can only reject the null hypothesis at 5% significance level

(B) Yes, corresponding 1 tailed test must lead to rejection of the null hypothesis because we know that the p value for a one tailed hypothesis is half of p value of a two tailed test.

So, if null hypothesis is rejected for a two tailed hypothesis test, then it must be rejected for one tailed test because it has half the p value of two tailed test.