The article "Supervised Exercise Versus Non-Supervised Exercise for Reducing Weight in Obese Adults" (J. Sport. Med. Phys. Fit., 2009: 85-90) reported on an investigation in which participants were randomly assigned either to a supervised exercise program or a control group. Those in the control group were told only that they should take measures to lose weight. After 4 months, the sample mean decrease in body fat for the 17 individuals in the experimental group was 6.2 kg with a sample standard deviation of 4.5 kg, whereas the sample mean and sample standard deviation for the 17 people in the control group were 1.7 kg and 3.1 kg, respectively. Assume normality of the two body fat loss distributions (as did the investigators). A, Calculate a 99% lower prediction bound for the body fat loss of a single randomly selected individual subjected to the supervised exercise program. Can you be highly confident that such an individual will actually lose body fat?
B. Does it appear that true average decrease in body fat is more than 2 kg larger for the experimental condition than for the control condition? Carry out a test of appropriate hypotheses using a significance level of .01