Question

State T OR F?

A)If a null hypothesis is rejected in favor of the alternative at the 1% level, then using the same data, it must be rejected in favor of the alternative at the 5% level.

B)If a null hypothesis is rejected against an alternative at the 5% level and at the 1% level, then you should report that the null was rejected at the 1% significance level. Reporting that it was also rejected at the 5% is redundant and not recommended.

Answer 1

A)

If a null hypothesis is rejected in favor of the alternative at the 1% level, it means that the p-value is less than 0.01

Then using the same data, the p-value would still be less than 0.05, so the null hypothesis must be rejected in favor of the alternative at the 5% level.

Hence True.

B)

If a null hypothesis is rejected against an alternative at the 1% level, it means that the p-value is less than 0.01.

This would imply that the p-value would still be less than 0.05, so the null hypothesis is rejected against an alternative at the 5% level as well.

So, reporting that it was also rejected at the 5% is redundant and not recommended.

Hence True.