9.1

Does this diet help? 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 24

pounds, with a sample standard deviation of 9 pounds. A second group of 39 people went on the diet but didn't exercise. After six months, their mean weight loss was 12 pounds, with a sample standard deviation of 8 pounds.

Construct a 90% confidence interval for the mean difference in weight losses. Let 1

denote the mean weight loss of the group with daily exercise. Use the TI-84 Plus calculator and round the answers to the nearest integer.

A 90% confidence interval for the mean difference in weight loss, in pounds, is ____<1-2<_____

More time on the Internet: A researcher polled a sample of 1052 adults in the year 2010, asking them how many hours per week they spent on the Internet. The sample mean was 10.19 with a standard deviation of 13.81. A second sample of 1022 adults was taken in the year 2012. For this sample, the mean was 10.87 with a standard deviation of 14.92. Assume these are simple random samples from populations of adults. Can you conclude that the mean number of hours per week spent on the Internet increased between 2010 and 2012? Let 1 denote the mean number of hours spent on the Internet in 2010. Use the =0.01 level and the P-value method with the TI-84 calculator.

State the appropriate null and alternate hypotheses.

H0:

H1:

This is a ________________ test.

Low-fat or low-carb? Are low-fat diets or low-carb diets more effective for weight loss? A sample of 48 subjects went on a low-carbohydrate diet for six months. At the end of that time, the sample mean weight loss was 2.9 kilograms with a sample standard deviation of 4.46 kilograms. A second sample of 46 subjects went on a low-fat diet. Their sample mean weight loss was 1.5

kilograms with a standard deviation of 3.44 kilograms. Can you conclude that the mean weight loss of subjects having low-carb diets is greater than the mean weight loss of subjects having low-fat diets? Let 1 denote the mean weight lost on the low-carb diet and 2 denote the mean weight lost on the low-fat diet. Use the =0.1 level and the TI-84 Plus calculator.

State the appropriate null and alternate hypotheses.

H0:

H1:

This is a _____________ test.

Contaminated water: The concentration of benzene was measured in units of milligrams per liter for a simple random sample of five specimens of untreated wastewater produced at a gas field. The sample mean was 7.2 with a sample standard deviation of 1.1. Seven specimens of treated wastewater had an average benzene concentration of 4.8 with a standard deviation of 2.5. It is reasonable to assume that both samples come from populations that are approximately normal. Can you conclude that the mean benzene concentration differs between treated water and untreated water? Let 1 denote the mean benzene concentration for untreated water and 2

denote the mean benzene concentration for treated water. Use the =0.10 level the P-value method with the TI-84 Plus calculator.

State the appropriate null and alternate hypotheses.

H0:

H1:

This is a _____________ test.