Probability and Statistics for Engineering and the Sciences
Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 12.4, Problem 56E

The article “Bone Density and Insertion Torque as Predictors of Anterior Cruciate Ligament Graft Fixation Strength” (The Amer. J. of Sports Med., 2004: 1421–1429) 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
Load 491 477 598 361 605 671 466 431
Torque 1.2 1.8 2.6 2.5 2.5 1.7 1.6
Load 384 422 [554 577 642 348 446
  1. a. Is it plausible that yield load is normally distributed?
  2. b. Estimate true average yield load by calculating a confidence interval with a confidence level of 95%, and interpret the interval.
  3. c. Here is output from Minitab for the regression of yield load on torque. Does the simple linear regression model specify a useful relationship between the variables?
Predictor Coef SE Coef T P
Constant 152.44 91.17 1.67 0.118
Torque 178.23 45 .97 3.88 0.002

Chapter 12.4, Problem 56E, The article Bone Density and Insertion Torque as Predictors of Anterior Cruciate Ligament Graft

Source DF SS MS F P
Regression 1 80554 80554 15.03 0. 002
Residual Error 13 69684 5360
Total 14 150238
  1. d. The authors of the cited paper state, “Consequently, we cannot but conclude that simple regression analysis-based methods are not clinically sufficient to predict individual fixation strength.” Do you agree? [Hint: Consider predicting yield load when torque is 2.0.]
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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…
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Chapter 12 Solutions

Probability and Statistics for Engineering and the Sciences

Ch. 12.1 - Suppose that in a certain chemical process the...Ch. 12.2 - Refer back to the data in Exercise 4, in which y =...Ch. 12.2 - The accompanying data on y = ammonium...Ch. 12.2 - Refer to the lank temperature-efficiency ratio...Ch. 12.2 - Values of modulus of elasticity (MOE, the ratio of...Ch. 12.2 - The article Characterization of Highway Runoff in...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - The following data is representative of that...Ch. 12.2 - The bond behavior of reinforcing bars is an...Ch. 12.2 - Wrinkle recovery angle and tensile strength are...Ch. 12.2 - Calcium phosphate cement is gaining increasing...Ch. 12.2 - a. Obtain SSE for the data in Exercise 19 from the...Ch. 12.2 - The invasive diatom species Didymosphenia geminata...Ch. 12.2 - Prob. 25ECh. 12.2 - Show that the point of averages (x,y) lies on the...Ch. 12.2 - Prob. 27ECh. 12.2 - a. Consider the data in Exercise 20. Suppose that...Ch. 12.2 - Consider the following three data sets, in which...Ch. 12.3 - Reconsider the situation described in Exercise 7,...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - Exercise 16 of Section 12.2 gave data on x =...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - For the past decade, rubber powder has been used...Ch. 12.3 - Refer back to the data in Exercise 4, in which y =...Ch. 12.3 - Misi (airborne droplets or aerosols) is generated...Ch. 12.3 - Prob. 37ECh. 12.3 - Refer to the data on x = liberation rate and y =...Ch. 12.3 - Carry out the model utility test using the ANOVA...Ch. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Verify that if each xi is multiplied by a positive...Ch. 12.3 - Prob. 43ECh. 12.4 - Fitting the simple linear regression model to the...Ch. 12.4 - Reconsider the filtration ratemoisture content...Ch. 12.4 - Astringency is the quality in a wine that makes...Ch. 12.4 - The simple linear regression model provides a very...Ch. 12.4 - Prob. 48ECh. 12.4 - You are told that a 95% CI for expected lead...Ch. 12.4 - Prob. 50ECh. 12.4 - Refer to Example 12.12 in which x = test track...Ch. 12.4 - Plasma etching is essential to the fine-line...Ch. 12.4 - Consider the following four intervals based on the...Ch. 12.4 - The height of a patient is useful for a variety of...Ch. 12.4 - Prob. 55ECh. 12.4 - The article Bone Density and Insertion Torque as...Ch. 12.5 - The article Behavioural Effects of Mobile...Ch. 12.5 - The Turbine Oil Oxidation Test (TOST) and the...Ch. 12.5 - Toughness and fibrousness of asparagus are major...Ch. 12.5 - Head movement evaluations are important because...Ch. 12.5 - Prob. 61ECh. 12.5 - Prob. 62ECh. 12.5 - Prob. 63ECh. 12.5 - The accompanying data on x = UV transparency index...Ch. 12.5 - Torsion during hip external rotation and extension...Ch. 12.5 - Prob. 66ECh. 12.5 - Prob. 67ECh. 12 - The appraisal of a warehouse can appear...Ch. 12 - Prob. 69SECh. 12 - Forensic scientists are often interested in making...Ch. 12 - Phenolic compounds are found in the effluents of...Ch. 12 - The SAS output at the bottom of this page is based...Ch. 12 - The presence of hard alloy carbides in high...Ch. 12 - The accompanying data was read from a scatterplot...Ch. 12 - An investigation was carried out to study the...Ch. 12 - Prob. 76SECh. 12 - Open water oil spills can wreak terrible...Ch. 12 - In Section 12.4, we presented a formula for...Ch. 12 - Show that SSE=Syy1Sxy, which gives an alternative...Ch. 12 - Suppose that x and y are positive variables and...Ch. 12 - Let sx and sy denote the sample standard...Ch. 12 - Verify that the t statistic for testing H0: 1 = 0...Ch. 12 - Use the formula for computing SSE to verify that...Ch. 12 - In biofiltration of wastewater, air discharged...Ch. 12 - Normal hatchery processes in aquaculture...Ch. 12 - Prob. 86SECh. 12 - Prob. 87SE
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