Physicians have been recommending more exercise for their patients, particularly those who are overweight. One benefit of regular exercise appears to be a reduction in cholesterol, a substance associated with heart disease. To study the relationship more carefully, a physician took a random sample of 50 patients who do not exercise and measured their cholesterol levels. He then started them on regular exercise programs. After 4 months, he asked each patient how many minutes per week (on average) he or she exercised; he also measured their cholesterol levels. Column 1 = weekly exercise in minutes, column 2 = cholesterol level before exercise program, and column 3 = cholesterol level after exercise program.

a. Do these data allow us to infer that the amount of exercise and the reduction in cholesterol levels are related?

b. Produce a 95% interval of the amount of cholesterol reduction for someone who exercises for 100 minutes per week.

c. Produce a 95% interval for the average cholesterol reduction for people who exercise for 120 minutes per week.