Using either the critical value rule or the p-value rule, if a one-sided null hypothesis for a single mean cannot be rejected at a given significance level, then the corresponding two-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.

Step-by-step explanation:

Using either the critical value rule or the p-value rule, a conclusion can be drawn at a level of significance (alpha)

The null hypothesis: u = hypothesized mean

Alternative hypothesis: u > u0 or u < u0 for a one tailed test

Alternative hypothesis for a two tailed test: u =/ u0

To draw a conclusion by failing to reject the null hypothesis as stated then: using critical value

Observed z score > critical z score for both the one and two tailed test.

Or using p value:

P-value > alpha for a one tailed test

P-value > alpha/2 for a two tailed test

Thus, if a one-sided null hypothesis for a single mean cannot be rejected at a given significance level, then the corresponding two-sided null hypothesis will also not be rejected at the same significance level.