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 70SE
Shoveling is not exactly a high-tech activity, but it will continue to be a required task even in our information age. The article “A Shovel with a Perforated Blade Reduces Energy Expenditure Required for Digging Wet Clay” (Human Factors, 2010: 492–502) reported on an experiment in which 13 workers were each provided with both a conventional shovel and a shovel whose blade was perforated with small holes. The authors of the cited article provided the following data on stable energy expenditure [(kcal/kg(subject)/lb(clay)]:
| Worker: | 1 | 2 | 3 | 4 |
| Conventional: | .0011 | .0014 | .0018 | .0022 |
| Perforated: | .0011 | .0010 | .0019 | .0013 |
| Worker: | 5 | 6 | 7 | |
| Conventional | .0010 | .0016 | .0028 | |
| Perforated: | .0011 | .0017 | .0024 | |
| Worker: | 8 | 9 | 10 | |
| Conventional: | .0020 | .0015 | .0014 | |
| Perforated: | .0020 | .0013 | .0013 | |
| Worker: | 11 | 12 | 13 | |
| Conventional: | .0023 | .0017 | .0020 | |
| Perforated: | .0017 | .0015 | .0013 |
a. Calculate a confidence interval at the 95% confidence level for the true average difference between energy expenditure for the conventional shovel and the perforated shovel (the relevant normal probability plot shows a reasonably linear pattern). Based on this interval, does it appear that the shovels differ with respect to true average energy expenditure? Explain.
b. Carry out a test of hypotheses at significance level .05 to see if true average energy expenditure using the conventional shovel exceeds that using the perforated shovel.
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Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
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