Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 8.3, Problem 13E
The article “Ultimate Load Analysis of Plate Reinforced Concrete Beams” (N. Subedi and P. Baglin, Engineering Structures, 2001:1068–1079) presents theoretical and measured ultimate strengths (in kN) for a sample of steel-reinforced concrete beams. The results are presented in the following table (two outliers have been deleted).
Let y denote the measured strength, x the theoretical strength, and t the true strength, which is unknown. Assume that y = t + ε, where ε is the measurement error. It is uncertain whether t is related to x by a linear model t = β0 + β1x or by a quadratic model t = β0 + β1x + β2x2.
- a. Fit the linear model y = β0 + β1x + ε. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0.
- b. Fit the quadratic model y = β0 + β1x + β2x2 + ε. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0.
- c. Plot the residuals versus the lilted values for the linear model.
- d. Plot the residuals versus the fitted values for the quadratic model.
- e. c. Based on the results in parts (a) through (d), which model seems more appropriate? Explain.
- f. Using the more appropriate model, estimate the true strength if the theoretical strength is 1500.
- g. Using the mom appropriate model, find a 95% confidence interval for the true strength if the theoretical strength is 1500.
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Q1A) List down the measures of central tendency and measures of dispersion 1)
Q1B) The operations manager of a plant that manufactures tires wants to compare the actual inner diameters of two grades of tires, each of which is expected to be 575 millimeters. A sample of five tires of each grade was selected, and the results representing the inner diameters of the tires, ranked from smallest to largest, are as follows.
Grade X
grade Y
568 570 575 578 584
573 574 575 577 578
requirement.
a) for each of the tow grades of tries, compute the mwan, median, and standred deviation.
b) which grade of tire providing better quality? explain.
c) what would be the effect on your answer in (a) and (b) if the last value for grade Y were 588 insert 578 explain.
PLEAS ANSWER Q1&B. THANK YOU.
The article “Ultimate Load Analysis of Plate Reinforced Concrete Beams” (N. Subedi and P. Baglin, Engineering Structures, 2001:1068–1079) presents theoretical and measured ultimate strengths (in kN) for a sample of steel reinforced concrete beams. The results are presented in the following table (two outliers have been deleted). Let y denote the measured strength, x the theoretical strength, and t the true strength, which is unknown. Assume that y = t + ε, where ε is the measurement error. It is uncertain whether t is related to x by a linear model t = β0 + β1x or by a quadratic model t = β0 + β1x + β2x2.
Fit the linear model y = β0 + β1x + ε. For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0.
a) The fitted linear model is?
b) Since (select one) P < 0.001 , 0.001 < P < 0.002 , 0.002 < P < 0.01 , 0.01 < P < 0.02 , 0.02 < P < 0.05 , 0.05 < P < 0.10 , 0.10 < P < 0.20 , 0.20 < P < 0.50…
Chapter 8 Solutions
Statistics for Engineers and Scientists
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