It is a common belief that college students gain an average of 15 pounds during their first year of college. In one study of 150 female first-year college students, the mean weight was 130.5 pounds at the beginning of the study and 131.8 pounds six months later. The standard deviation of weights was about 30 pounds at each time, and the change in weight scores for the 150 freshmen had a standard deviation of 3 pounds. Complete parts a through c. a. Explain how this standard deviation, 3, could be so much less than the standard deviation of 30 for the weight scores at each time. Choose the correct answer below. A. Even though there is a lot of variability among the initial and final weights of the women, most women see a large change in weight over the course of the study. B. Despite there being little variability among the initial and final weights of the women, most women do not see a large change in weight over the course of the study. C. Despite there being little variability among the initial and final weights of the women, most women see a large change in weight over the course of the study. D. Even though there is a lot of variability among the initial and final weights of the women, most women do not see a large change in weight over the course of the study. b. Is 15 pounds a plausible mean weight change in the population of freshman women? Construct a 95% confidence interval for the population mean change in weight (weight after the study minus initial weight), then interpret the results. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to three decimal places as needed.) A. Yes, because 15 pounds does not lie in the confidence interval (.). B. Yes, because 15 pounds lies in the confidence interval (.) . C. No, because 15 pounds does not lie in the confidence interval (0.8 1.9 D. No, because 15 pounds lies in the confidence interval ().