Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 9, Problem 68SE
The article “Supervised Exercise Versus Non- Supervised Exercise for Reducing Weight in Obese Adults” (The J. of Sports Med. and Physical Fitness, 2009: 85–90) reported on an investigation in which participants were randomly assigned to either 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 weight-loss distributions (as did the investigators).
a. Calculate a 99% lower prediction bound for the weight 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 weight?
b. Does it appear that true average decrease in body fat is more than two kg larger for the experimental condition than for the control condition? Use the accompanying Minitab output to reach a conclusion at significance level of .01. [Note: Minitab accepts such summary data as well as individual observations. Also, because the test is upper-tailed, the software provides a lower confidence bound rather than a conventional CI.]
| Sample | N | Mean | StDev | SE Mean |
| Exptl. | 17 | 6.20 | 4.50 | 1.1 |
| Control | 17 | 1.70 | 3 .10 | 0.75 |
Difference 5 mu (1) 2 mu (2)
Estimate for difference: 4.50
95% lower bound for difference: 2.25
T-Test of difference 5 2 (vs >):
T-Value 5 1.89
P-Value 5 0.035 DF 5 28
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Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
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