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.
-A farmer has decided to use a new additive to grow his crops. He divided his farm into 10 plots and kept records of the corn yield (in bushels) before and after using the additive. The results are shown below. $$\begin{array} { | l c c c c c c c c c c | }
\hline \text { Plot: } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \
\hline \text { Before } & 9 & 9 & 8 & 7 & 6 & 8 & 5 & 9 & 10 & 11 \
\text { After } & 10 & 9 & 9 & 8 & 7 & 10 & 6 & 10 & 10 & 12 \
\hline
\end{array}$$ You wish the test the following hypothesis at the 5 percent 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 $1.833 .$
B) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.833$ or less than $1.833$.
C) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.833$.
D) Reject $\mathrm { H } _ { 0 }$ if test statistic is less than $1.833$.

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.
-A farmer has decided to use a new additive to grow his crops. He divided his farm into 10 plots and kept records of the corn yield (in bushels) before and after using the additive. The results are shown below. $$\begin{array} { | l c c c c c c c c c c | } 
\hline \text { Plot: } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \
\hline \text { Before } & 9 & 9 & 8 & 7 & 6 & 8 & 5 & 9 & 10 & 11 \
\text { After } & 10 & 9 & 9 & 8 & 7 & 10 & 6 & 10 & 10 & 12 \
\hline
\end{array}$$ You wish the test the following hypothesis at the 5 percent 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 $1.833 .$
B) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.833$ or less than $1.833$.
C) Reject $\mathrm { H } _ { 0 }$ if test statistic is greater than $- 1.833$.
D) Reject $\mathrm { H } _ { 0 }$ if test statistic is less than $1.833$.

Quizplus · Accepted Answer

The null hypothesis is $H_0: \mu_d = 0$, and the alternative hypothesis is $H_1: \mu_d > 0$. This is a right-tailed test, so we will reject the null hypothesis if the test statistic is greater than the critical value. The critical value for a right-tailed test with a significance level of 0.05 and 9 degrees of freedom is 1.833. Therefore, we will reject the null hypothesis if the test statistic is greater than 1.833.

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