Refer to the previous exercise. Suppose that the change in weight scores for the 132 freshmen had a standard deviation of 2.0 pounds.
a. Explain how this standard deviation could be so much less than the standard deviation of 30 for the weight scores at each time.
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.
c. What assumptions are necessary for the inference in part b?

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