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

question 23

Multiple Choice

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. We wish to compare the means of two populations using paired observations. Suppose that $\bar { d } = 3.125 , s _ { d } = 2.911$ , and $n = 8$ , and that you wish to test the following hypothesis at the $10 \%$ level of significance:
$H _ { 0 } : \mu _ { d } = 0 \text { against } H _ { 1 } : \mu _ { d } > 0 .$
What decision rule would you use?

• A) Reject \(H _ { 0 }\) if the test statistic is less than 1.415.
• B) Reject \(H _ { 0 }\) if the test statistic is greater than \(- 1.145\).
• C) Reject \(H _ { 0 }\) if the test statistic is greater than \(- 1.145\) or less than 1.415.
• D) Reject \(H _ { 0 }\) if the test statistic is greater than \(1.415\).