37. At a certain university, the Electrical Engineering faculty decides to teach a course on robot intelligence using two different methods, one an existing method and the other a method using new strategies. The faculty randomly selects two sections of students who are scheduled to take this course. One section is taught using the existing method, while the other uses the new method. At the end of the semester, both sections are given the same test. Their test scores produce the following summary statistics:

n1 = 49, ¯X1 = 79, S2 1 = 30 n2 = 45, ¯X2 = 86, S2 2 = 40 350 8 Estimation of Population Parameters

(a) Find a 95% confidence interval for the difference μ1 − μ2 of the two population means.

(b) Find a 98% lower confidence interval for the difference μ1 − μ2 of the two population means and then find a 98% upper one-sided confidence interval for the difference μ1 − μ2 of the two population means.