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

question 70

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 $1 \%$ level of significance:
$$\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0 \text { against } \mathrm { H } _ { 1 } : \mu _ { \mathrm { d } } > 0 \text {. }$$
What decision rule would you use?

• A) Reject \(\mathrm { H } _ { 0 }\) if test statistic is greater than \(2.998\).
• B) Reject \(\mathrm { H } _ { 0 }\) if test statistic is greater than \(- 2.998\).
• C) Reject \(\mathrm { H } _ { 0 }\) if test statistic is greater than \(- 2.998\) and less than \(2.998\).
• D) Reject \(\mathrm { H } _ { 0 }\) if test statistic is less than \(2.998\).

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Definitions:

Decision Making

The cognitive process of selecting a course of action from among multiple alternatives.

Team Performance

The level of productivity, efficiency, and quality achieved by a group working together towards common goals or tasks.

Contingency Anchor

A concept in decision-making and planning that deals with uncertainties by identifying and preparing for potential variations from expected outcomes or conditions.

Diagnose

The process of identifying the nature of a problem, issue, or situation through analysis of its symptoms or characteristics.