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

question 46

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 $\overline { \mathrm { d } } = 3.125$ , $\mathrm { S } _ { \mathrm { d } } = 2.911$ , and $\mathrm { n } = 8$ , and that you wish to test the following hypothesis at the $10 \%$ level of significance:
$\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0$ against $\mathrm { H } _ { 1 } : \mu _ { \mathrm { d } } > 0$ What decision rule would you use?

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

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