Consider a test for If the Pvalue is such that you can reje

Consider a test for . If the P-value is such that you can reject H0 for = .01, can you always reject H0 for = .05? Explain your answer.
No. If the P-value lies below 0.01 you would reject at the 1% level of significance, but not at the 5% level.
Yes. If the P-value lies below 0.01 you would reject at the 1% level of significance, but not at the 5% level.
No. If the P-value lies above 0.05 you would reject at the 1% level of significance and at the 5% level.
Yes. If H0 is rejected at the 1% level it will always be rejected at the 5% level.

Solution

Yes, because p-value less than 0.01 implies p-value is less than 0.05, thus

{Yes. If H0 is rejected at the 1\\% level it will always be rejected at the 5\\% level.}