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.

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.

Step-by-step 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.