Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Textbook Question
Chapter 12.2, Problem 20E
The bond behavior of reinforcing bars is an important determinant of strength and stability. The article “Experimental Study on the Bond Behavior of Reinforcing Bars Embedded in Concrete Subjected to Lateral Pressure” (J. of Materials in Civil Engr., 2012:125–133) reported the results of one experiment in which varying levels of lateral pressure were applied to 21 concrete cube specimens, each with an embedded 16-mm plain steel round bar. and the corresponding bond capacity was determined. Due to differing concrete cube strengths (fcu, in MPa), the applied lateral pressure was equivalent to a fixed proportion of the specimen’s (0, .1fcu, … , .6fcu). Also, since bond strength can be heavily influenced by the specimen’s fcu, bond capacity was expressed as the ratio of bond strength (MPa) to 
.
| Pressure | 0 | 0 | 0 | .1 | .1 | .1 | .2 |
| Ratio | 0.123 | 0.100 | 0.101 | 0.172 | 0.133 | 0.107 | 0.217 |
| Pressure | .2 | .2 | .3 | .3 | .3 | .4 | .4 |
| Ratio | 0.172 | 0.151 | 0.263 | 0.227 | 0.252 | 0.310 | 0.365 |
| Pressure | .4 | .5 | .5 | .5 | .6 | .6 | .6 |
| Ratio | 0.239 | 0.365 | 0.319 | 0.312 | 0.394 | 0.386 | 0.320 |
- a. Does a
scatterplot of the data support the use of the simple linear regression model? - b. Use the accompanying Minitab output to give point estimates of the slope and intercept of the population regression line.
- c. Calculate a point estimate of the true average bond capacity when lateral pressure is .45fcu.
- d. What is a point estimate of the error standard deviation σ, and how would you interpret it?
- e. What is the value of total variation, and what proportion of it can be explained by the model relationship?
The regression equation is
Ratio = 0.101 + 0.461 Pressure
| Predictor | Coef | SE Coef | T | P |
| Constant | 0.10121 | 0.01308 | 7.74 | 0.000 |
| Pressure | 0.46071 | 0.03627 | 12.70 | 0.000 |
Analysis of Variance
| Source | DF | SS | MS | F | P |
| Regression | 1 | 0.17830 | 0.17830 | 161.37 | 0.000 |
| Residual Error | 19 | 0.02099 | 0.00110 | ||
| Total | 20 | 0.19929 |
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Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
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