Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis.
-Suppose you wish to test the claim that $\mu _ { \mathrm { d } }$ , the mean value of the differences d for a population of paired data, is greater than 0 . Given a sample of $\mathrm { n } = 15$ and a significance level of $\alpha = 0.01$ , what criterion would be used for rejecting the null hypothesis?

Question

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis. -Suppose you wish to test the claim that $\mu _ { \mathrm { d } }$, the mean value of the differences d for a population of paired data, is greater than 0 . Given a sample of $\mathrm { n } = 15$ and a significance level of $\alpha = 0.01$, what criterion would be used for rejecting the null hypothesis? A) Reject null hypothesis if test statistic $> 2.602$. B) Reject null hypothesis if test statistic $> 2.977$ or $< - 2.977$. C) Reject null hypothesis if test statistic $< 2.624$. D) Reject null hypothesis if test statistic $> 2.624$.

Quizplus · Accepted Answer

Since we are testing whether the mean value of differences d is greater than 0, this is a one-tailed test with the alternative hypothesis being $\mu _ { \mathrm { d } }> 0$. We need to find the critical value for a one-tailed test with a significance level of $\alpha = 0.01$ and degrees of freedom ($df$) equal to 14 (n-1=15-1=14) using a t-distribution table. The critical value is 2.624. Therefore, we will reject the null hypothesis if the test statistic is greater than 2.624. Option D is the only one that correctly represents this decision criterion.

Determine the Decision Criterion for Rejecting the Null Hypothesis in the Given