Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 7.4, Problem 4E
The depth of wetting of a soil is the depth to which water content will increase owing to external factors. The article “Discussion of Method for Evaluation of Depth of Wetting in Residential Areas” (J. Nelson, K. Chao, and D. Overton, Journal of Geotechnical and Geoenvironmental Engineering, 2011:293–296) discusses the relationship between depth of wetting beneath a structure and the age of the structure. The article presents measurements of depth of wetting, in meters, and the ages, in years, of 21 houses, as shown in the following table.
- a. Compute the least-squares line for predicting depth of wetting (y) from age (x).
- b. Identify a point with an unusually large x-value. Compute the least-squares line that results from deletion of this point.
- c. Identify another point which can be classified as an outlier. Compute the least-squares line that results from deletion of the outlier, replacing the point with the unusually large x-value.
- d. Which of these two points is more influential? Explain.
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The depth of wetting of a soil is the depth to which water content will increase owing to
extemal factors. The article "Discussion of Method for Evaluation of Depth of Wetting in
Residential Areas" (J. Nelson, K. Chao, and D. Overton, Journal of Geotechnical and
Geoenvironmental Engineering, 2011:293-296) discusses the relationship between depth of
wetting beneath a structure and the age of the structure. The article presents measurements
of depth of wetting, in meters, and the ages, in years, of 21 houses, as shown in the
following table.
Age
Depth
7.6
4
4.6
6.1
9.1
3
4.3
7.3
5.2
10.4
15.5
5.8
10.7
4
5.5
6.1
10.7
10.4
4.6
7.0
6.1
14
16.8
10
9.1
8.8
Compute the least-squares line for predicting depth of wetting (y) from age (x).
b. Identify a point with an unusually large x-value. Compute the least-squares line that
results from deletion of this point.
Identify another point which can be classified as an outlier. Compute the least-squares
line that results from deletion of the outlier,…
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 "Experimental Measurement of Radiative Heat Transfer in Gas-Solid
Suspension Flow System" (G. Han, K. Tuzla, and J. Chen, AIChe Journal, 2002:1910-
1916) discusses the calibration of a radiometer. Several measurements were made on the
electromotive force readings of the radiometer (in volts) and the radiation flux (in kilowatts
per square meter). The results (read from a graph) are presented in the following table.
Heat flux (y)
15 31 51 55 67 89
Signal output (x) 1.08 2.42 4.17 4.46 5.17 6.92
Compute the least-squares line for predicting heat flux from the signal output.
If the radiometer reads 3.00 V, predict the heat flux.
If the radiometer reads 8.00 V, should the heat flux be predicted? If so, predict it. If
not, explain why.
C.
Chapter 7 Solutions
Statistics for Engineers and Scientists
Ch. 7.1 - Compute the correlation coefficient for the...Ch. 7.1 - For each of the following data sets, explain why...Ch. 7.1 - For each of the following scatterplots, state...Ch. 7.1 - True or false, and explain briefly: a. If the...Ch. 7.1 - In a study of ground motion caused by earthquakes,...Ch. 7.1 - A chemical engineer is studying the effect of...Ch. 7.1 - Another chemical engineer is studying the same...Ch. 7.1 - Tire pressure (in kPa) was measured for the right...Ch. 7.1 - Prob. 10ECh. 7.1 - The article Drift in Posturography Systems...
Ch. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - A scatterplot contains four points: (2, 2), (1,...Ch. 7.2 - Each month for several months, the average...Ch. 7.2 - In a study of the relationship between the Brinell...Ch. 7.2 - A least-squares line is fit to a set of points. If...Ch. 7.2 - Prob. 4ECh. 7.2 - In Galtons height data (Figure 7.1, in Section...Ch. 7.2 - In a study relating the degree of warping, in mm....Ch. 7.2 - Moisture content in percent by volume (x) and...Ch. 7.2 - The following table presents shear strengths (in...Ch. 7.2 - Structural engineers use wireless sensor networks...Ch. 7.2 - The article Effect of Environmental Factors on...Ch. 7.2 - An agricultural scientist planted alfalfa on...Ch. 7.2 - Curing times in days (x) and compressive strengths...Ch. 7.2 - Prob. 13ECh. 7.2 - An engineer wants to predict the value for y when...Ch. 7.2 - A simple random sample of 100 men aged 2534...Ch. 7.2 - Prob. 16ECh. 7.3 - A chemical reaction is run 12 times, and the...Ch. 7.3 - Structural engineers use wireless sensor networks...Ch. 7.3 - Prob. 3ECh. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - The coefficient of absorption (COA) for a clay...Ch. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Three engineers are independently estimating the...Ch. 7.3 - In the skin permeability example (Example 7.17)...Ch. 7.3 - Prob. 12ECh. 7.3 - In a study of copper bars, the relationship...Ch. 7.3 - Prob. 14ECh. 7.3 - In the following MINITAB output, some of the...Ch. 7.3 - Prob. 16ECh. 7.3 - In order to increase the production of gas wells,...Ch. 7.4 - The following output (from MINITAB) is for the...Ch. 7.4 - The processing of raw coal involves washing, in...Ch. 7.4 - To determine the effect of temperature on the...Ch. 7.4 - The depth of wetting of a soil is the depth to...Ch. 7.4 - Good forecasting and control of preconstruction...Ch. 7.4 - The article Drift in Posturography Systems...Ch. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - A windmill is used to generate direct current....Ch. 7.4 - Two radon detectors were placed in different...Ch. 7.4 - Prob. 11ECh. 7.4 - The article The Selection of Yeast Strains for the...Ch. 7.4 - Prob. 13ECh. 7.4 - The article Characteristics and Trends of River...Ch. 7.4 - Prob. 15ECh. 7.4 - The article Mechanistic-Empirical Design of...Ch. 7.4 - An engineer wants to determine the spring constant...Ch. 7 - The BeerLambert law relates the absorbance A of a...Ch. 7 - Prob. 2SECh. 7 - Prob. 3SECh. 7 - Refer to Exercise 3. a. Plot the residuals versus...Ch. 7 - Prob. 5SECh. 7 - The article Experimental Measurement of Radiative...Ch. 7 - Prob. 7SECh. 7 - Prob. 8SECh. 7 - Prob. 9SECh. 7 - Prob. 10SECh. 7 - The article Estimating Population Abundance in...Ch. 7 - A materials scientist is experimenting with a new...Ch. 7 - Monitoring the yield of a particular chemical...Ch. 7 - Prob. 14SECh. 7 - Refer to Exercise 14. Someone wants to compute a...Ch. 7 - Prob. 16SECh. 7 - Prob. 17SECh. 7 - Prob. 18SECh. 7 - Prob. 19SECh. 7 - Use Equation (7.34) (page 545) to show that 1=1.Ch. 7 - Use Equation (7.35) (page 545) to show that 0=0.Ch. 7 - Prob. 22SECh. 7 - Use Equation (7.35) (page 545) to derive the...
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