Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 8.2, Problem 1E
In an experiment to determine factors related to weld toughness, the Charpy V-notch impact toughness in ft·lb (y) was measured for 22 welds at 0°C, along with the lateral expansion at the notch in % (x1), and the brittle fracture surface in % (x2). The data are presented in the following table.
- a. Fit the model y = β0 + β1x1 + ε. For each coefficient, test the null hypothesis that it is equal to 0.
- b. Fit the model y = β0 + β1x2 + ε. For each coefficient, test the null hypothesis that it is equal to 0.
- c. Fit the model y = β0 + β1x1 + β2x2 + ε. For each coefficient, test the null hypothesis that it is equal to 0.
- d. Which of the models in parts (a) through (c) is the best of the three? Why do you think so?
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In an experiment to determine factors related to weld toughness, the Charpy V-notch impact
toughness in ft - 1b (v) was measured for 22 welds at 0°Č, along with the lateral expansion
at the notch in % (x,), and the brittle fracture surface in % (x2). The data are presented in the
following table.
X1
X2
y
32
20.0
28
39
23.0
28
20
12.8
32
21
16.0
29
25
10.2
31
20
11.6
28
32
17.6
25
29
17.8
28
27
16.0
29
43
26.2
27
22
9.6
32
22
15.2
32
18
8.8
43
32
20.4
24
22
12.2
36
25
14.6
36
25
10.4
29
20
11.6
30
20
12.6
31
24
16.2
36
18
9.2
34
28
16.8
30
a. Fit the model y = Bo + B1 X1 + ɛ. For each coefficient, test the null hypothesis that it is
equal to 0.
b. Fit the model y = Bo + B, xz + ɛ. For each coefficient, test the null hypothesis that it is
equal to 0.
c. Fit the model y = Bo + B1 X1 + Bzx2 + ɛ. For each coefficient, test the null hypothesis
that it is equal to 0.
d. Which of the models in parts (a) through (c) is the best of the three? Why do you think
%3D
+ E.
so?
Computer chips often contain surface imperfections.For a certain type of computer chip, theprobability mass function of the number of defects X is presented in the following table.
An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.18 kgf/cm2 for the
modified mortar (m = 42) and y = 16.86 kgf/cm for the unmodified mortar (n = 30). Let µ1 and Hz be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions
are both normal.
(a) Assuming that o1 = 1.6 and o2 = 1.3, test Ho: µ1 - 42 = 0 versus H3: µ1 – 42 > 0 at level 0.01.
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z =
P-value =
State the conclusion in the problem context.
Fail to reject Ho: The data does not suggest that the difference in average tension bond strengths exceeds from 0.
o Reject Ho: The data does not suggest that the difference in average tension bond…
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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