Two statistics teachers both believe that each has the smarter class. To put this to the test, they give the same final exam to their students. A summary of the class sizes, class means, and standard deviations is given below:

$$\begin{array}{lll} n_1 = 37, & \bar{x}_1 = 83.1, & s_1 = 17.9 \\ n_2 = 46, & \bar{x}_2 = 82.5, & s_2 = 18.1 \\ \end{array}$$

Is there evidence, at an $\alpha = 0.03$ level of significance, to conclude that there is a difference in the two classes? (Assume that the population variances are equal.) Carry out an appropriate hypothesis test, filling in the information requested.

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