Chapter 10.4, Problem 55PB

Checking for freshman 15 Refer to the previous exercise. Suppose that the change in weight scores for the 132 freshmen had a standard deviation of 2.0 pounds.

1. a. Explain how this standard deviation could be so much less than the standard deviation of 30 for the weight scores at each time.
2. b. Is 15 pounds a plausible mean weight change in the population of freshman women? Answer by constructing a 95% confidence interval for the population mean change in weight or conducting a significance test of the hypothesis that the mean weight change in the population equals 15. Interpret.
3. c. What assumptions are necessary for the inference in part b?

10.54 Freshman 15 a myth? The freshman 15 is the name of a common belief that college students, particularly women, gain an average of 15 pounds during their first year of college. A recent study (Journal of American Health, vol. 58, 2009, pp. 223–231) found that female students weighed an average of 133.0 pounds at the start of the school year and an average of 135.1 pounds at the end of the school year. The standard deviation of weights was about 30 pounds at each time. Other reports have been consistent with this finding.

1. a. Estimate the change in the mean weight.
2. b. Is this sufficient information to find a confidence interval or conduct a test about the change in the mean? If not, what else do you need to know?