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 $1.415$.

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 $\overline { \mathrm { d } } = 3.125$, $\mathrm { S } _ { \mathrm { d } } = 2.911$, 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 $1.415$.

Quizplus · Accepted Answer

Since the alternate hypothesis is one-tailed (specifically, greater than 0), we need to find the critical value from the t-distribution with (n-1) degrees of freedom and alpha level of 0.10.

Using a t-table or calculator, we find the critical value to be approximately 1.415.

Therefore, we would reject the null hypothesis if the test statistic is greater than 1.415 (i.e. falls in the rejection region).

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