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 \(1.415\).

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Definitions:

Collect Like Terms

In algebra, the process of combining terms that have the same variables raised to the same power into a single term.

Operation Indicated

Definition: The specific arithmetic operation (such as addition, subtraction, multiplication, division) suggested or required by a problem or equation.

Simplify

To make something easier to understand or apply by reducing complexity.

Collect Like Terms

The process of simplifying an algebraic expression by combining terms that have the same variables.