Applied Statistics in Business and Economics
5th Edition
ISBN: 9781259329050
Author: DOANE
Publisher: MCG
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Chapter 12, Problem 41CE
To determine
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Question 4
An article in Quality Progress (May 2011, pp. 42-48) describes the use of factorial experiments to improve a
silver powder production process. This product is used in conductive pastes to manufacture a wide variety of
products ranging from silicon wafers to elastic membrane switches. Powder density (g/cm²) and surface area
(cm/g) are the two critical characteristics of this product. The experiments involved three factors: reaction
temperature, ammonium percentage, stirring rate. Each of these factors had two levels, and the design was
replicated twice. The design is shown in Table 3.
A222222222222233
Stir Rate
(RPM)
Ammonium
(%)
Table 3: Silver Powder Experiment from Exercise 13.23
Temperature
(°C)
Density
Surface Area
100
8
14.68
0.40
100
8
15.18
0.43
30
100
8
15.12
0.42
30
100
17.48
0.41
150
7.54
0.69
150
8
6.66
0.67
30
150
8
12.46
0.52
30
150
8
12.62
0.36
100
40
10.95
0.58
100
40
17.68
0.43
30
100
40
12.65
0.57
30
100
40
15.96
0.54
150
40
8.03
0.68
150
40
8.84
0.75
30
150…
-
+
++
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
བྱ॰༤༠སྦྱོ སྦྱོཋཏྟཱུ
a
b
ab
11.635 12.089
17.273 17.815
с
ас
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…
Chapter 12 Solutions
Applied Statistics in Business and Economics
Ch. 12.1 - Prob. 1SECh. 12.1 - Prob. 2SECh. 12.1 - Prob. 3SECh. 12.1 - Prob. 4SECh. 12.1 - Prob. 5SECh. 12.1 - Prob. 6SECh. 12.2 - (a) Interpret the slope of the fitted regression...Ch. 12.2 - (a) Interpret the slope of the fitted regression...Ch. 12.2 - Prob. 9SECh. 12.2 - (a) Interpret the slope of the fitted regression...
Ch. 12.2 - (a) Interpret the slope of the fitted regression...Ch. 12.3 - Prob. 12SECh. 12.3 - Prob. 13SECh. 12.3 - The regression equation Credits = 15.4 .07 Work...Ch. 12.3 - Below are fitted regressions for Y = asking price...Ch. 12.3 - Refer back to the regression equation in exercise...Ch. 12.3 - Refer back to the regression equation in exercise...Ch. 12.4 - Instructions for exercises 12.18 and 12.19: (a)...Ch. 12.4 - Instructions for exercises 12.18 and 12.19: (a)...Ch. 12.4 - Instructions for exercises 12.2012.22: (a) Use...Ch. 12.4 - Instructions for exercises 12.2012.22: (a) Use...Ch. 12.4 - Instructions for exercises 12.2012.22: (a) Use...Ch. 12.5 - Instructions for exercises 12.23 and 12.24: (a)...Ch. 12.5 - Prob. 24SECh. 12.5 - A regression was performed using data on 32 NFL...Ch. 12.5 - A regression was performed using data on 16...Ch. 12.6 - Prob. 27SECh. 12.6 - Prob. 28SECh. 12.6 - Instructions for exercises 12.2912.31: (a) Use...Ch. 12.6 - Instructions for exercises 12.2912.31: (a) Use...Ch. 12.6 - Instructions for exercises 12.2912.31: (a) Use...Ch. 12.7 - Refer to the Weekly Earnings data set below. (a)...Ch. 12.7 - Prob. 33SECh. 12.8 - Prob. 34SECh. 12.8 - Prob. 35SECh. 12.9 - An estimated regression for a random sample of...Ch. 12.9 - An estimated regression for a random sample of...Ch. 12.9 - Prob. 38SECh. 12.9 - Prob. 39SECh. 12 - (a) How does correlation analysis differ from...Ch. 12 - (a) What is a simple regression model? (b) State...Ch. 12 - (a) Explain how you fit a regression to an Excel...Ch. 12 - (a) Explain the logic of the ordinary least...Ch. 12 - (a) Why cant we use the sum of the residuals to...Ch. 12 - Prob. 6CRCh. 12 - Prob. 7CRCh. 12 - Prob. 8CRCh. 12 - Prob. 9CRCh. 12 - Prob. 10CRCh. 12 - Prob. 11CRCh. 12 - Prob. 12CRCh. 12 - (a) What is heteroscedasticity? Identify its two...Ch. 12 - (a) What is autocorrelation? Identify two main...Ch. 12 - Prob. 15CRCh. 12 - Prob. 16CRCh. 12 - (a) What is a log transform? (b) What are its...Ch. 12 - Prob. 40CECh. 12 - Prob. 41CECh. 12 - Prob. 42CECh. 12 - Prob. 43CECh. 12 - Prob. 44CECh. 12 - Prob. 45CECh. 12 - Prob. 46CECh. 12 - Prob. 47CECh. 12 - Prob. 48CECh. 12 - Prob. 49CECh. 12 - Prob. 50CECh. 12 - Prob. 51CECh. 12 - Prob. 52CECh. 12 - Prob. 53CECh. 12 - Prob. 54CECh. 12 - Prob. 55CECh. 12 - Prob. 56CECh. 12 - Prob. 57CECh. 12 - Prob. 58CECh. 12 - Prob. 59CECh. 12 - In the following regression, X = weekly pay, Y =...Ch. 12 - Prob. 61CECh. 12 - In the following regression, X = total assets (...Ch. 12 - Prob. 63CECh. 12 - Below are percentages for annual sales growth and...Ch. 12 - Prob. 65CECh. 12 - Prob. 66CECh. 12 - Prob. 67CECh. 12 - Simple regression was employed to establish the...Ch. 12 - Prob. 69CECh. 12 - Prob. 70CECh. 12 - Prob. 71CECh. 12 - Below are revenue and profit (both in billions)...Ch. 12 - Below are fitted regressions based on used vehicle...Ch. 12 - Below are results of a regression of Y = average...
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