8.32 Anorexia in teenage girls A study4 compared various therapies for teenage girls suffering from anorexia, an eating disorder. For each girl, weight was measured before and after a fixed period of treatment. The variable measured was the change in weight, X = weight at the end of the study minus weight at the beginning of the study. The therapies were designed to aid weight gain, corresponding to positive values of X. For the sample of 17 girls receiving the family therapy, the changes in weight during the study were 11, 11, 6, 9, 14, -3, 0, 7, 22, -5, -4, 13, 13, 9, 4, 6, 11.

a. Plot these with a dot plot or box plot and summarize.

b. Using the web app, software or a calculator, show that the weight changes have x = 7.29 and s = 7.18 pounds.

c. Using the web app, software or a calculator, show that the standard error of the sample mean was se = 1.74.

d. To use the t distribution, explain why the 95% confidence interval uses the t-score equal to 2.120.

e. Let m denote the population mean change in weight for this therapy. Using results from parts

b, c, and

d, show that the 95% confidence interval for m is (3.6, 11.0).
Explain why this suggests that the true mean change in weight is positive but possibly quite small.