Probability and Statistics for Engineering and the Sciences STAT 400 - University Of Maryland
9th Edition
ISBN: 9781305764477
Author: Jay L. Devore
Publisher: Cengage Learning
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Textbook Question
Chapter 15.4, Problem 27E
In an experiment to study the way in which different anesthetics affect plasma epinephrine concentration, ten dogs were selected and concentration was measured while they were under the influence of the anesthetics isoflurane, halothane, and cyclopropane (“Sympathoadrenal and Hemodynamic Effects of Isoflurane, Halothane, and Cyclopropane in Dogs,” Anesthesiology, 1974:465-470). Test at level .05 to see whether there is an anesthetic effect on concentration.
| Dog | |||||
| 1 | 2 | 3 | 4 | 5 | |
| Isoflurane | .28 | .51 | 1.00 | .39 | .29 |
| Halothane | .30 | .39 | .63 | .38 | .21 |
| Cyclopropane | 1.07 | 1.35 | .69 | .28 | 1.24 |
| 6 | 7 | 8 | 9 | 10 | |
| Isoflurane | .36 | .32 | .69 | .17 | .33 |
| Halothane | .88 | .39 | .51 | .32 | .42 |
| Cyclopropane | 1.53 | .49 | .56 | 1.02 | .30 |
Expert Solution & Answer
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Table 2: Crack Experiment for Exercise 2
A B C D Treatment Combination
(1)
Replicate
I II
7.037
6.376
14.707 15.219
|++++ 1
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a
b
ab
11.635 12.089
17.273 17.815
с
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10.403 10.151
4.368 4.098
bc
abc
9.360 9.253
13.440 12.923
d
8.561 8.951
ad
16.867 17.052
bd
13.876 13.658
abd
19.824 19.639
cd
11.846 12.337
acd
6.125
5.904
bcd
11.190 10.935
abcd
15.653 15.053
Question 3
Continuation of Exercise 2. One of the variables in the experiment described in Exercise 2, heat treatment
method (C), is a categorical variable. Assume that the remaining factors are continuous.
(a) Write two regression models for predicting crack length, one for each level of the heat treatment method
variable. What differences, if any, do you notice in these two equations?
(b) Generate appropriate response surface contour plots for the two regression models in part (a).
(c) What set of conditions would you recommend for the factors A, B, and D if you use heat treatment method
C = +?
(d) Repeat…
Question 2
A nickel-titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially
serious problem in the final part because it can lead to nonrecoverable failure. A test is run at the parts producer
to determine the effect of four factors on cracks. The four factors are: pouring temperature (A), titanium content
(B), heat treatment method (C), amount of grain refiner used (D). Two replicates of a 24 design are run, and
the length of crack (in mm x10-2) induced in a sample coupon subjected to a standard test is measured. The
data are shown in Table 2.
1
(a) Estimate the factor effects. Which factor effects appear to be large?
(b) Conduct an analysis of variance. Do any of the factors affect cracking? Use a = 0.05.
(c) Write down a regression model that can be used to predict crack length as a function of the significant
main effects and interactions you have identified in part (b).
(d) Analyze the residuals from this experiment.
(e) Is there an…
A 24-1 design has been used to investigate the effect of four factors on the resistivity of a silicon wafer. The data
from this experiment are shown in Table 4.
Table 4: Resistivity Experiment for Exercise 5
Run
A
B
с
D
Resistivity
1
23
2
3
4
5
6
7
8
9
10
11
12
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0
0
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33.2
4.6
31.2
9.6
40.6
162.4
39.4
158.6
63.4
62.6
58.7
0
0
60.9
3
(a) Estimate the factor effects. Plot the effect estimates on a normal probability scale.
(b) Identify a tentative model for this process. Fit the model and test for curvature.
(c) Plot the residuals from the model in part (b) versus the predicted resistivity. Is there any indication on
this plot of model inadequacy?
(d) Construct a normal probability plot of the residuals. Is there any reason to doubt the validity of the
normality assumption?
Chapter 15 Solutions
Probability and Statistics for Engineering and the Sciences STAT 400 - University Of Maryland
Ch. 15.1 - Give as much information as you can about the...Ch. 15.1 - Here again is the data on expense ratio (%) for a...Ch. 15.1 - The accompanying data is a subset of the data...Ch. 15.1 - A random sample of 15 automobile mechanics...Ch. 15.1 - Both a gravimetric and a spectrophotometric method...Ch. 15.1 - Reconsider the situation described in Exercise 39...Ch. 15.1 - Use the large-sample version of the Wilcoxon test...Ch. 15.1 - Reconsider the port alcohol content data from...Ch. 15.1 - Prob. 9ECh. 15.2 - Prob. 10E
Ch. 15.2 - Prob. 11ECh. 15.2 - The article A Study of Wood Stove Particulate...Ch. 15.2 - The urinary fluoride concentration (parts per...Ch. 15.2 - Prob. 14ECh. 15.2 - The article Measuring the Exposure of Infants to...Ch. 15.2 - Prob. 16ECh. 15.3 - Prob. 17ECh. 15.3 - Compute the 99% signed-rank interval for true...Ch. 15.3 - Prob. 19ECh. 15.3 - Prob. 20ECh. 15.3 - Prob. 21ECh. 15.3 - Compute a 99% CI for 1 2 using the data in...Ch. 15.4 - The accompanying data refers to concentration of...Ch. 15.4 - Prob. 24ECh. 15.4 - Prob. 25ECh. 15.4 - Prob. 26ECh. 15.4 - In an experiment to study the way in which...Ch. 15 - The article Effects of a Rice-Rich Versus...Ch. 15 - Prob. 29SECh. 15 - The given data on phosphorus concentration in...Ch. 15 - Prob. 31SECh. 15 - Prob. 32SECh. 15 - The sign test is a very simple procedure for...Ch. 15 - Prob. 34SECh. 15 - Prob. 35SECh. 15 - Prob. 36SE
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