1. Two microprocessors are compared on 6 benchmark codes to determine whether there is a difference in speed. The times (in seconds) used by each processor on each code are as follows. Find a 95% confidence interval for the difference between the mean speeds and interpret this interval in the context of the problem.
2 3 4
Processor
A 27.2 18.1 27.2 19.7 24.5 22.1
Processor B
24.1 19.3 26.8 20.1 27.6 29.8
2. In a survey of adults with diabetes, the average body mass index (BMI) in a sample of 1924 women was 31.1 with a standard deviation of 0.2. The BMI in a sample of 1559 men was 30.4 with a standard deviation of 0.6. Construct a 99% confidence interval for the difference in the mean BMI between women and men with diabetes and interpret this interval in the context of the problem.
3. Traffic engineers compared rates of traffic accidents at intersections with raised medians with rates at intersections with two-way left-turn lanes. They found that out of 4644 accidents at intersections with raised medians, 2280 were rear-end accidents and out of 4584 accidents at two-way left-turn lanes, 1982 were rear-end accidents. Construct a 95% confidence interval for the difference between the proportions of accidents that are of the rear-end type at the two types of intersections and interpret this interval in the context of the problem.
4. A group of 78 people enrolled in a weight-loss program that involved adhering to a special diet and to a daily exercise program. After six months, their mean weight loss was 25 pounds, with a sample standard deviation of 9 pounds. A second group of 43 people went on the diet but didn’t exercise. After six months, their mean weight less was 14 pounds with a sample standard deviation of 7 pounds. Construct a 95% confidence interval for the mean difference in weight loss and interpret this interval in the context of the problem.
