Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 8.1, Problem 4E
The article “Application of Analysis of Variance to Wet Clutch Engagement” (M. Mansouri, M. Khonsari, et al., Proceedings of the Institution of Mechanical Engineers, 2002:117–125) presents the following fitted model for predicting clutch engagement time in seconds (y) from engagement starting speed in m/s (x1), maximum drive torque in N·m (x2), system inertia in kg m2 (x3), and applied force rate in kN/s (x4):
The sum of squares for regression was SSR = 1.08613 and the sum of squares for error was SSE = 0.036310. There were 44 degrees of freedom for error.
- a. Predict the clutch engagement time when the starting speed is 20 m/s, the maximum drive torque is 17 N·m, the system inertia is 0.006 kg·m2, and the applied force rate is 10 kN/s.
- b. Is it possible to predict the change in engagement time associated with an increase of 2 m/s in starting speed? If so, find the predicted change. If not, explain why not.
- c. Is it possible to predict the change in engagement time associated with an increase of 2 N·m in maximum drive torque? If so, find the predicted change. If not, explain why not.
- d. Compute the coefficient of determination R2.
- e. Compute the F statistic for testing the null hypothesis that all the coefficients are equal to 0. Can this hypothesis be rejected?
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Students have asked these similar questions
The article "Application of Analysis of Variance to Wet Clutch Engagement" (M.
Mansouri, M. Khonsari, et al., Proceedings of the Institution of Mechanical Engineers,
2002:117-125) presents the following fitted model for predicting clutch engagement time in
seconds (y) from engagement starting speed in m/s (x1), maximum drive torque in N · m
(x2), system inertia in kg · m² (x3), and applied force rate in kN/s (x4):
y = -0.83 + 0.017.x, + 0.0895x, + 42.77.xz + 0.027x, – 0.0043x,x,
The sum of squares for regression was SSR = 1.08613 and the sum of squares for error was
SSE = 0.036310. There were 44 degrees of freedom for error.
Predict the clutch engagement time when the starting speed is 20 m/s, the maximum
drive torque is 17 N·m, the system inertia is 0.006 kg · m², and the applied force rate
is 10 kN/s.
b. Is it possible to predict the change in engagement time associated with an increase of 2
m/s in starting speed? If so, find the predicted change. If not, explain why not.
Is it…
The article "Influence of Freezing Temperature on Hydraulic Conductivity of Silty Clay" (J.
Konrad and M. Samson, Journal of Geotechnical and Geoenvironmental Engineering,
2000:180–187) describes a study of factors affecting hydraulic conductivity of soils. The
measurements of hydraulic conductivity in units of 108 cm/s (y), initial void ratio (x), and
thawed void ratio (x2) for 12 specimens of silty clay are presented in the following table.
y
1.01 1.12 1.04 1.30 1.01 1.04 0.955 1.15 1.23 1.28 1.23 1.30
0.84 0.88 0.85 0.95 0.88 0.86 0.85 0.89 0.90 0.94 0.88 0.90
X1
0.81 0.85 0.87 0.92 0.84 0.85 0.85 0.86 0.85 0.92 0.88 0.92
X2
Fit the model y = Bo + fix1 + e. For each coefficient, test the null hypothesis that it is
equal to 0.
Fit the model y = Bo + Bzx2 + e. For each coefficient, test the null hypothesis that it is
equal to 0.
Fit the model y = Bo + BzX1 + Bzxz + e. For each coefficient, test the null hypothesis that
it is equal to 0.
d. Which of the models in parts (a) to (c) is…
The following table presents measurements of mean noise levels in dBA (y), roadway width
in m (x1), and mean speed in km/h (x2), for 10 locations in Bangkok, Thailand, as reported
in the article "Modeling of Urban Area Stop-and-Go Traffic Noise" (P. Pamanikabud and
C. Tharasawatipipat, Journal of Transportation Engineering, 1999:152–159).
y
X1
X2
78.1
6.0
30.61
78.1
10.0
36.55
79.6
12.0
36.22
81.0
6.0
38.73
78.7
6.5
29.07
78.1
12.0
28.26
78.6
6.5
30.28
78.5
6.5
30.25
78.4
9.0
29.03
79.6
6.5
33.17
Construct a good linear model to predict mean noise levels using roadway width, mean
speed, or both, as predictors. Provide the standard deviations of the coefficient estimates
and the P-values for testing that they are different from 0. Explain how you chose your
model.
Chapter 8 Solutions
Statistics for Engineers and Scientists
Ch. 8.1 - In an experiment to determine the factors...Ch. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - The article Application of Analysis of Variance to...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Refer to Exercise 7. a. Find a 95% confidence...Ch. 8.1 - In a study of the lung function of children, the...Ch. 8.1 - Prob. 10E
Ch. 8.1 - Prob. 11ECh. 8.1 - The following MINITAB output is for a multiple...Ch. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - The following data were collected in an experiment...Ch. 8.1 - The November 24, 2001, issue of The Economist...Ch. 8.1 - The article Multiple Linear Regression for Lake...Ch. 8.1 - Prob. 19ECh. 8.2 - In an experiment to determine factors related to...Ch. 8.2 - In a laboratory test of a new engine design, the...Ch. 8.2 - In a laboratory test of a new engine design, the...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.3 - True or false: a. For any set of data, there is...Ch. 8.3 - The article Experimental Design Approach for the...Ch. 8.3 - Prob. 3ECh. 8.3 - An engineer measures a dependent variable y and...Ch. 8.3 - Prob. 5ECh. 8.3 - The following MINITAB output is for a best subsets...Ch. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - (Continues Exercise 7 in Section 8.1.) To try to...Ch. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - The article Ultimate Load Analysis of Plate...Ch. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - The article Modeling Resilient Modulus and...Ch. 8.3 - The article Models for Assessing Hoisting Times of...Ch. 8 - The article Advances in Oxygen Equivalence...Ch. 8 - Prob. 2SECh. 8 - Prob. 3SECh. 8 - Prob. 4SECh. 8 - In a simulation of 30 mobile computer networks,...Ch. 8 - The data in Table SE6 (page 649) consist of yield...Ch. 8 - Prob. 7SECh. 8 - Prob. 8SECh. 8 - Refer to Exercise 2 in Section 8.2. a. Using each...Ch. 8 - Prob. 10SECh. 8 - The data presented in the following table give the...Ch. 8 - The article Enthalpies and Entropies of Transfer...Ch. 8 - Prob. 13SECh. 8 - Prob. 14SECh. 8 - The article Measurements of the Thermal...Ch. 8 - The article Electrical Impedance Variation with...Ch. 8 - The article Groundwater Electromagnetic Imaging in...Ch. 8 - Prob. 18SECh. 8 - Prob. 19SECh. 8 - Prob. 20SECh. 8 - Prob. 21SECh. 8 - Prob. 22SECh. 8 - The article Estimating Resource Requirements at...Ch. 8 - Prob. 24SE
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