Question

Using the critical value rule, if a two-sided null hypothesis cannot be rejected for a single mean at a given significance level, then the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ______________ be rejected at the same significance level.

Answer 1

If the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.

Explanation:

When we performed a two-sided test and the null hypothesis failed to be rejected, when we perform a one-sided test we may reject or not the null hypothesis.

For instance, we have a 5% significance level test, where the test statistic is z=1.8.

For a two-sided test the critical values for α=5% are zc=±1.960. In this situation, the null hypothesis failed to be rejected.

But if we perform a one-sided test with the same significance level, we have a critical value z=1.645 and the conclusion is that the null hypothesis is rejected.

Then, if the null hypothesis is failed to be rejected in a two-sided test, we are not sure if a one-sided test will reject or not the null hypothesis, at the same significance level.

We are only sure that if a two-sided test rejects the null hypothesis, a one-side test with same significance level will always reject the null hypothesis.