Question

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.

always

sometimes

never

Answer 1

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 never be rejected at the same significance level.

Answer: never

Note: For one tailed test, if the null hypothesis is not rejected at a given significance level . That means, p-value is greater than .

implies that, p-value is also greater than in a two-tailed and we do not reject the null hypothesis. Because, In two-tailed test,

p-value = 2 * p-value in one-tailed.