Question

32. If a one-sided null hypothesis is 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. never

B. always

C. sometimes

Answer 1

Q.32)

If a one-sided null hypothesis is 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 sometimes rejected at the same significance level.

Note: Suppose we used significance level of 0.05

case 1) if p-value for one-tailed test is 0.01, which is less than 0.05 so, we reject the null hypothesis.

And for two-tailed we get, p-value = 2 * 0.01 = 0.02, which is less than 0.05. So, in this case we reject the null.

case 2) if p-value for one-tailed test is 0.04, which is less than 0.05 so, we reject the null hypothesis.

And for two-tailed we get, p-value = 2 * 0.04 = 0.08 which is greater than 0.05. So, in this case we do not reject the null.