Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.3, Problem 33E
During oil drilling operations, components of the drilling assembly may suffer from sulfide stress cracking. The article “Composition Optimization of High-Strength Steels for Sulfide Cracking Resistance Improvement” (Corrosion Science, 2009: 2878–2884) reported on a study in which the composition of a standard grade of steel was analyzed. The following data on y = threshold stress (% SMYS) and x = yield strength (MPa) was read from a graph in the article (which also included the equation of the least squares line).
| x | 635 | 644 | 711 | 708 | 836 | 820 | 810 | 870 | 856 | 923 | 878 | 937 | 948 |
| y | 100 | 93 | 88 | 84 | 77 | 75 | 74 | 63 | 57 | 55 | 47 | 43 | 38 |
- a. What proportion of observed variation in stress can be attributed to the approximate linear relationship between the two variables?
- b. Compute the estimated standard deviation
- c. Calculate a confidence interval using confidence level 95% for the expected change in stress associated with a 1 MPa increase in strength. Does it appear that this true average change has been precisely estimated?
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2
9.6
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9.7
96.4
8.8
4
8.5
10.8
89
10.1
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10.3
10.9
88
9.6
6
10.6
10.6
103.8
8.6
7
11.8
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147.3
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Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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