An anger$-$management course claims that, after completing its seminar, participants will lose their tempers less often. Always a skeptic, you decide to test this claim. A random sample of $12$

seminar participants is chosen, and these participants are asked to record the number of times that they lost their tempers in the two weeks prior to the course. After the course is over, the same participants are asked to record the number of times that they lost their tempers in the next two weeks. The following table lists the results of the survey. Using these data, test the claim at the $0\mathrm{.}01$

level of significance assuming that the population distribution of the paired differences is approximately normal. Let participants before completing the anger$-$management course be Population $1$ and let participants after completing the anger$-$management course be Population $2.$

Number of Times Temper Was Lost during a Two$-$Week Period

Before $12$

$12$

$3$

$8$

$10$

$7$

$4$

$10$

$12$

$4$

$12$

$10$

After $12$

$9$

$4$

$9$

$8$

$7$

$5$

$8$

$7$

$4$

$10$

$5$

Step $2$ of $3$ : Compute the value of the test statistic. Round your answer to three decimal places.