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 different from 0. Given a sample of n = 23 and a significance level of $\alpha =$ 0.05, 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 different from 0. Given a sample of n = 23 and a significance level of $\alpha =$ 0.05, what criterion would be used for rejecting the null hypothesis? A) Reject null hypothesis if test statistic $> 1.717$. B) Reject null hypothesis if test statistic $> 2.074$ or $< - 2.074$. C) Reject null hypothesis if test statistic $> 2.069$ or $< - 2.069$. D) Reject null hypothesis if test statistic $> 1.717$ or $< - 1.717$.

Quizplus · Accepted Answer

Since the claim is that the mean difference is different from 0, this is a two-tailed test. With $n = 23$ (degrees of freedom $n-1 = 22$) and $\alpha = 0.05$, the critical values for a two-tailed test from a t-distribution table are approximately $\pm 2.074$. Thus, the null hypothesis is rejected for test statistics greater than 2.074 or less than -2.074.

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