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 .

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. 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 .

Quizplus · Accepted Answer

Given the hypothesis test is one-tailed ($H_1: \mu_d > 0$) and at the 10% significance level, we reject $H_0$ if the test statistic is in the upper tail of the distribution, specifically greater than the critical value. The correct decision rule involves rejecting $H_0$ if the test statistic exceeds a certain positive value, which aligns with option D.

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