You wish to test the following claim ($\displaystyle {H}_{{a}}$) at a significance level of $\displaystyle \alpha={0.002}$. For the context of this problem, $\displaystyle \mu_{{d}}=\mu_{{2}}-\mu_{{1}}$ where the first data set represents a pre-test and the second data set represents a post-test.     

$\displaystyle {H}_{{o}}:\mu_{{d}}={0}$
$\displaystyle {H}_{{a}}:\mu_{{d}}\ne{0}$

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for $\displaystyle {n}={39}$ subjects. The average difference (post - pre) is $\displaystyle \overline{{d}}={9.1}$ with a standard deviation of the differences of $\displaystyle {s}_{{d}}={17.3}$.

1. What is the test statistic for this sample?
   
   test statistic = Round to 3 decimal places.
   
   
2. What is the p-value for this sample? Round to 4 decimal places.
   
   p-value =
   
   
3. The p-value is...
   • less than (or equal to) $\displaystyle \alpha$
   • greater than $\displaystyle \alpha$
   
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
   • There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is not equal to 0.
   • The sample data support the claim that the mean difference of post-test from pre-test is not equal to 0.
   • There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is not equal to 0.