Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 9, Problem 6SE
a.
To determine
Find all the main and interaction effects.
b.
To determine
Construct an ANOVA table and the find the
c.
To determine
Check whether the data indicate that there are any interactions between the weight percent of Al2O3 and the weight percent of C4S3.
d.
To determine
Check whether the data convincingly demonstrate that the Fe2O3/CaO ratio depends on the weight percent of Al2O3.
e.
To determine
Check whether the data convincingly demonstrate that the Fe2O3/CaO ratio depends on the weight percent of C4S3.
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The article "Simulation of the Hot Carbonate Process for Removal of CO, and H,S from
Medium Btu Gas" (K. Park and T. Edgar, Energy Progress, 1984:174–180) presents an
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Reaction
Estimated Experimental
Difference
45.10
42.95
2.15
2
85.77
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151.84
146.17
5.67
4.
244.30
228.22
16.08
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257.67
240.63
17.04
6
44.32
41.99
2.33
84.41
82.05
2.36
8
150.47
149.62
0.85
253.81
245.45
8.36
Find a 95% confidence interval for the mean difference between the estimated and actual
pressures.
The article "Oxidation State and Activities of Chromium Oxides in Cao-SiO,-CrO, Slag
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2002:595-603) presents the amount x (in mole percent) and activity coefficient y of CrO,5
for several specimens. The data, extracted from a larger table, are presented in the following
table.
х
У
2.6
10.20
5.03
19.9
8.84
0.8
6.62
5.3
2.89
20.3
2.31
39.4
7.13
5.8
3.40
29.4
5.57
2.2
7.23
5.5
2.12
33.1
1.67
44.2
5.33
13.1
16.70
0.6
9.75
2.2
2.74
16.9
2.58
35.5
1.50
48.0
Compute the least-squares line for predicting y from x.
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Compute the least-squares line for predicting y from 1/x.
d. Plot the residuals versus the fitted values.
C.
Using the better fitting line, find a 95% confidence interval for the mean value of y
when x= 5.0.
The article "Experimental Design Approach for the Optimization of the Separation of
Enantiomers in Preparative Liquid Chromatography" (S. Lai and Z. Lin, Separation Science
and Technology, 2002: 847–875) describes an experiment involving a chemical process
designed to separate enantiomers. A model was fit to estimate the cycle time (y) in terms of
the flow rate (x1), sample concentration (x2), and mobile-phase composition (x3). The results
of a least-squares fit are presented in the following table. (The article did not provide the
value of the t statistic for the constant term.)
Predictor
Coefficient
т
Constant
1.603
X1
-0.619
-22.289
0.000
X2
0.086
3.084
0.018
0.306
11.011
0.000
0.272
8.542
0.000
0.057
1.802
0.115
0.105
3.300
0.013
X1X2
-0.022
-0.630
0.549
XXз
-0.036
-1.004
0.349
X>Xз
0.036
1.018
0.343
Of the following, which is the best next step in the analysis?
i.
Nothing needs to be done. This model is fine.
Drop x;, x;, and x from the model, and then perform an F test.
iii. Drop…
Chapter 9 Solutions
Statistics for Engineers and Scientists
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