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# The article “Ultimate Load Analysis of Plate Reinforced ISBN: 9780073401331 38

## Solution for problem 13E Chapter 8.3

Statistics for Engineers and Scientists | 4th Edition

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Problem 13E

The article “Ultimate Load Analysis of Plate Reinforced Concrete Beams” (N. Subcdi 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 or by a quadratic model Theoretical Measured Theoretical Measured 991 1118 1516 1550 785 902 1071 1167 1195 1373 1480 1609 1021 1196 1622 1756 1285 1609 2032 2119 1167 1413 2032 2237 1519 1668 660 640 1314 1491 565 530 1743 1952 738 893 791 844 682 775

a. Fit the linear model For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0.

b. Fit the quadratic model For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0.

c. Plot the residuals versus the fitted values for the linear model.

d. Plot the residuals versus the fitted values for the quadratic model.

e. 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 more appropriate model, find a 95% confidence interval for the true strength if the theoretical strength is 1500.

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BIO375:Genetics WINTERSEMESTER2017 INSTRUCTOR:DR.ALEXYNIKITIN nikitina@gvsu.edu 09 January 2017 Lecture 1: Introduction to Genetics I. Fundamental Concepts in Genetics A. Genetics is the study of inheritance and variation B. Genes are the fundamental unit of heredity C. Genes come in multiple forms called...

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##### ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. Since the solution to 13E from 8.3 chapter was answered, more than 251 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 13E from chapter: 8.3 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. This full solution covers the following key subjects: model, Strength, theoretical, measured, coefficient. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The answer to “The article “Ultimate Load Analysis of Plate Reinforced Concrete Beams” (N. Subcdi 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 + ?, where ? is the measurement error. It is uncertain whether t is related to x by a linear model or by a quadratic model TheoreticalMeasuredTheoreticalMeasured991111815161550785902107111671195137314801609102111961622175612851609203221191167141320322237151916686606401314149156553017431952738893791844682775a. Fit the linear model For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0.________________b. Fit the quadratic model For each coefficient, find the P-value for the null hypothesis that the coefficient is equal to 0.________________c. Plot the residuals versus the fitted values for the linear model.________________d. Plot the residuals versus the fitted values for the quadratic model.________________e. 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 more appropriate model, find a 95% confidence interval for the true strength if the theoretical strength is 1500.” is broken down into a number of easy to follow steps, and 209 words.

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