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If a two-sided null hypothesis is not rejected for a single mean at a given significance...

If a two-sided null hypothesis is not rejected for a single mean at a given significance level, 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. Always

B. Sometimes

C. Never

Math   Statistics-And-Probability   
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Answer #1

B. Sometimes

If a two-sided null hypothesis is not rejected for a single mean at a given significance level, 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.

The p-value for the two tailed test will be double than the one tailed test. So, if the p-value for the two tailed test is lower than the twice the significance level, then two tailed test will not be rejected and one tailed test will be rejected at the same level of significance.

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