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.
A)Always
B)Sometimes
C)Never

Question

Quizplus · Accepted Answer

If a one-sided null hypothesis cannot be rejected, then it means that the p-value corresponding to the observed test statistic is greater than the significance level. For example, if we have a one-sided null hypothesis that the mean is greater than or equal to a certain value, and we cannot reject it at a significance level of 0.05, then the p-value must be greater than 0.05. If we now look at the corresponding two-sided null hypothesis, then it means that we are testing whether the mean is equal to a certain value (i.e., both greater than or equal to and less than or equal to the value). Since the one-sided null hypothesis could not be rejected, it means that the observed test statistic did not provide strong evidence for the mean being greater than or equal to the value. It follows that there is even less evidence to suggest that the mean is either greater than or equal to or less than or equal to the value, and thus, the corresponding two-sided null hypothesis cannot be rejected at the same significance level. In general, rejecting a two-sided null hypothesis requires stronger evidence than rejecting a one-sided null hypothesis at the same significance level.

If a One-Sided Null Hypothesis for a Single Mean Cannot