Professor Professorson, a researcher at Greendale Community College, is interested in the effect of caffeine on the typing speed of students. Professorson obtains a random sample of 8 students who are given 400 mg of caffeine then given a typing test. They type an average of 51.4 words per minute (wpm), with a sample standard deviation of 12.3 wpm. He also obtains a random sample of 13 students who are given a placebo before the typing test. The placebo group types an average of 43.9 wpm, with a sample standard deviation of 15.1 wpm. Assume typing speeds follow a normal distribution in both groups.

(a) Construct a 99% confidence interval for μC-μP, the true difference in average typing speed between the caffeine and placebo groups. Assume that the true variances are equal.

(b) Construct a 99% confidence interval for μC-μP, the true difference in average typing speed between the caffeine and placebo groups. Do not assume that the true variances are equal.