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 $\bar { d } = 3.125 , \mathrm {~S} _ { \mathrm { d } } =$ $2.911$, and $\mathrm { n } = 8$, and that you wish to test the following hypothesis at the 5 percent level of significance:
$$\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0 \text { against } \mathrm { H } _ { 1 } : \boldsymbol { \mu } _ { \mathrm { d } } 0 \text {. }$$
What decision rule would you use?
A) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.895$ and less than $1.895$.
B) Reject $\mathrm { H } _ { 0 }$ if test statistic is less than $1.895$.
C) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $1.895$.
D) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.895$.

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 $\bar { d } = 3.125 , \mathrm {~S} _ { \mathrm { d } } =$ $2.911$, and $\mathrm { n } = 8$, and that you wish to test the following hypothesis at the 5 percent level of significance:
$$\mathrm { H } _ { 0 } : \mu _ { \mathrm { d } } = 0 \text { against } \mathrm { H } _ { 1 } : \boldsymbol { \mu } _ { \mathrm { d } } > 0 \text {. }$$
What decision rule would you use?
A) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.895$ and less than $1.895$.
B) Reject $\mathrm { H } _ { 0 }$ if test statistic is less than $1.895$.
C) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $1.895$.
D) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.895$.

Quizplus · Accepted Answer

The decision rule for a one-tailed test (right-tailed, since we're testing if $\mu_d > 0$) at the 5 percent level of significance with $n = 8$ (degrees of freedom = 7) involves rejecting the null hypothesis if the test statistic is greater than the critical value from the t-distribution table. Since the hypothesis test is right-tailed, we reject $H_0$ if the test statistic is greater than the critical value, which for a 5% significance level and 7 degrees of freedom is approximately 1.895.

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