A psychologist is studying the effect of a stress management workshop on anxiety levels. Eight participants took an anxiety test before and after attending the workshop. Their scores are as follows:

a. Using a $0.01$ significance level, test the claim that the mean anxiety score before the workshop is higher than after the workshop.
b. Construct the $99\%$ confidence interval for the mean difference. What does this interval indicate about anxiety change?
c. What can you conclude about the effectiveness of the workshop?

Test statistic $t=23.01$, critical value $t_{0.01,7}=2.998$

$99\%$ confidence interval:

The workshop significantly reduced anxiety levels

Test statistic $t=1.85$, critical value $t_{0.01,7}=2.998$

$99\%$ confidence interval:

There is no significant evidence that the workshop reduced anxiety

Test statistic $t=23.01$, critical value $t_{0.01,7}=2.998$

$99\%$ confidence interval:

The workshop significantly increased anxiety levels

Test statistic $t=2.44$, critical value $t_{0.01,7}=3.31$

$99\%$ confidence interval:

There is weak evidence the workshop had an effect on anxiety