Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 5.3, Problem 11E
The article “Effect of Granular Subbase Thickness on Airfield Pavement Structural Response” (K. Gopalakrishnan and M. Thompson, Journal of Materials in Civil Engineering, 2008:331–342) presents a study of the effect of the subbase thickness on the amount of surface deflection caused by aircraft landing on an airport runway. In six applications of a 160 kN load on a runway with a subbase thickness of 864 mm, the average surface deflection was 2.03 mm with a standard deviation of 0.090 mm. Find a 90% confidence interval for the
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The article "Effect of Granular Subbase Thickness on Airfield Pavement Structural
Response" (K. Gopalakrishnan and M. Thompson, Journal of Materials in Civil
Engineering, 2008:331-342) presents a study of the amount of surface deflection caused by
aircraft landing on an airport runway. A load of 160 kN was applied to a runway surface,
and the amount of deflection in mm (y) was measured at various distances in m (x) from the
point of application. The results are presented in the following table.
y
0.000
3.24
0.305
2.36
0.610
1.42
0.914
0.87
1.219
0.54
1.524
0.34
1.830
0.24
a.
Fit the linear model y = Bo + B1x + ɛ. For each coefficient, test the hypothesis that the
coefficient is equal to 0.
b. Fit the quadratic model y = Bo + Bịx + B2x² + ɛ. For each coefficient, test the hypothesis
that the coefficient is equal to 0.
%3D
Fit the cubic model y = Bo + B1x +
B2x? + B3x + E. For each coefficient, test the
C.
hypothesis that the coefficient is equal to 0.
d.
Which of the models in parts (a)…
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 article "Modeling Resilient Modulus and Temperature Correction for Saudi Roads" (H.
Wahhab, I. Asi, and R. Ramadhan, Journal of Materials in Civil Engineering, 2001:298–
305) describes a study designed to predict the resilient modulus of pavement from physical
properties. The following table presents data for the resilient modulus at 40°Cin10® kPa (y),
the surface area of the aggregate in m²/kg (x1), and the softening point of the asphalt in °C
(х).
y
X1
X2
1.48
5.77
60.5
1.70
7.45
74.2
2.03
8.14
67.6
2.86
8.73
70.0
2.43
7.12
64.6
3.06
6.89
65.3
2.44
8.64
66.2
1.29
6.58
64.1
3.53
9.10
68.6
1.04
8.06
58.8
1.88
5.93
63.2
1.90
8.17
62.1
1.76
9.84
68.9
2.82
7.17
72.2
1.00
7.78
54.1
The full quadratic model is y = + P,x, + PzX, + Pz*jXz + Pxx¡ + Bzx; + €. Which
submodel of this full model do you believe is most appropriate? Justify your answer by
fitting two or more models and comparing the results.
Chapter 5 Solutions
Statistics for Engineers and Scientists
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