You wish to test the following claim ($H_a$) at a significance level of $\alpha = 0.01$. For the context of this problem, $\mu_d = \mu_2 - \mu_1$ where the first data set represents a pre-test and the second data set represents a post-test.
$H_o: \mu_d = 0$
$H_a: \mu_d < 0$
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 $n = 8$ subjects. The average difference (post - pre) is $\bar{d} = -20.2$ with a standard deviation of the differences of $s_d = 20.4$.
What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = -2.998
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic = -2.800