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.

a. never

b. sometimes

c. always

Answer 1

If a two sided null hypothesis cannot be rejected, this doesn't mean that one sided will not be rejected. One sided may be rejected depending on the p-value.

In case of one sided, the p-value calculated is the half of the p-value calculated in two sided hypothesis. hence there could be chance that p-value < significance level. This will lead to the rejection of null hypothesis.

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 sometimes be rejected at the same significance level.

Option B