A company that sponsors LSAT prep courses would like to be able to claim that their courses improve scores by at least 3 percentage points. To test this, they take a sample of 8 people, have each take an initial diagnostic test, then take the prep course, and then take a post-test after the course. The test results are below (scores are out of 100%):

$$\begin{array}{ccc} \mbox{Person} & \mbox{Initial Test} & \mbox{Post-Test} \\ 1 & 64 & 67 \\ 2 & 72 & 79 \\ 3 & 63 & 66 \\ 4 & 76 & 86 \\ 5 & 80 & 91 \\ 6 & 71 & 78 \\ 7 & 64 & 63 \\ 8 & 75 & 81 \\ \end{array}$$

Is there evidence, at an $\alpha = 0.03$ level of significance, to conclude that the prep course improves scores by at least 3 percentage points? Carry out an appropriate hypothesis test, filling in the information requested. (Arrange your data so that the standardized test statistic is for the change from the initial test to the post-test.)

A. The value of the standardized test statistic:

Note: For the next part, your answer should use interval notation. An answer of the form $(-\infty, a)$ is expressed (-infty, a), an answer of the form $(b, \infty)$ is expressed (b, infty), and an answer of the form $(-\infty, a) \cup (b, \infty)$ is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Reject $H_0$.
B. Reject $H_1$.
C. Do Not Reject $H_1$.
D. Do Not Reject $H_0$.