Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 9.3, Problem 36E
Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded condition and an abraded condition (“The Effect of Wet Abrasive Wear on the Tensile Properties of Cotton and Polyester-Cotton Fabrics,” J. Testing and Evaluation, 1993: 84–93). Use the paired t test, as did the authors of the cited article, to test H0: μD = 0
versus Ha: μD .> 0 at significance level .01.
| Fabric | |||||||
| 1 | 2 | 3 | 4 5 | 6 | 7 | 8 | |
| U | 36.4 | 55.0 | 51.5 | 38.7 43.2 | 48.8 | 25.6 | 49.8 |
| A | 28.5 | 20.0 | 46.0 | 34.5 36.5 | 52.5 | 26.5 | 46.5 |
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The article “Effect of Internal Gas Pressure on the Com- pression Strength of Beverage Cans and Plastic Bottles” (J. of Testing and Evaluation, 1993: 129–131) includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola. Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. What assumptions are necessary for your analysis? ( use ? = 0.01 )
Artificial joints consist of a ceramic ball mounted on a taper. The article "Friction in
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of the Institution of Mechanical Engineers, 2000: 685-692) presents data on the coefficient
of friction for a push-on load of 2 kN for taper assemblies made from two zirconium alloys
and employing three different neck lengths. Five measurements were made for each
combination of material and neck length. The results presented in the following table are
consistent with the cell means and standard deviations presented in the article.
Тарег
Material
Neck
Length
Coefficient of Friction
CPTI-ZIO2
CPTI-Z:O,
CPTI-Z:O, Long
TIAlloy-ZrO, Short
TiAlloy-ZrO, Medium
TiAlloy-ZrO, Long
Short
0.254 0.195 0.281 0.289 0.220
Medium
0.196 0.220 0.185 0.259 0.197
0.329 0.481 0.320 0.296 0.178
0.150 0.118 0.158 0.175 0.131
0.180 0.184 0.154 0.156 0.177
0.178 0.198 0.201 0.199 0.210
Compute the main effects and interactions.
Construct…
The article "Bone Density and Insertion Torque as Predictors of Anterior Cruciate Ligament Graft Fixation Strength"t gave the accompanying data on maximum insertion torque (N• m) and yield load (N), the latter being one
measure of graft strength, for 15 different specimens.
Torque
1.8
2.2
1.9
1.3
2.1
2.2
1.6
2.1
1.2
1.8
2.6
2.5
2.5
1.7
1.6
Load
491
477
598
361
605
671 466
431
384
422
554
577
642
348
446
(a) Is it plausible that yield load is normally distributed?
Yes, there are more than thirty data values.
No, a normal probability plot of yield load is not quite linear.
Yes, a normal probability plot of yield load is quite quadratic.
No, there is not more than thirty data values.
Yes, a normal probability plot of yield load is quite linear.
(b) Estimate true average yield load by calculating a confidence interval with a confidence level of 95%. (Round your answer to two decimal places.)
Interpret the interval.
We are 95% confident that the true population average yield load lies below…
Chapter 9 Solutions
Probability and Statistics for Engineering and the Sciences
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