ELEMENTARY STATS. 18 WEEK ACCESS CODE
13th Edition
ISBN: 9780135900826
Author: Triola
Publisher: PEARSON
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Chapter 3.1, Problem 34BSC
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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 3 Solutions
ELEMENTARY STATS. 18 WEEK ACCESS CODE
Ch. 3.1 - Average The defunct website IncomeTaxList.com...Ch. 3.1 - Whats Wrong? USA Today published a list consisting...Ch. 3.1 - Measures of Center In what sense are the mean,...Ch. 3.1 - Resistant Measures Here are four of the Verizon...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...
Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - Critical Thinking. For Exercises 5-20, watch out...Ch. 3.1 - In Exercises 21-24, find the mean and median for...Ch. 3.1 - In Exercises 21-24, find the mean and median for...Ch. 3.1 - In Exercises 21-24, find the mean and median for...Ch. 3.1 - In Exercises 21-24, find the mean and median for...Ch. 3.1 - Large Data Sets from Appendix B. In Exercises...Ch. 3.1 - Large Data Sets from Appendix B. In Exercises...Ch. 3.1 - Large Data Sets from Appendix B. In Exercises...Ch. 3.1 - Large Data Sets from Appendix B. In Exercises...Ch. 3.1 - In Exercises 29-32, find the mean of the data...Ch. 3.1 - In Exercises 29-32, find the mean of the data...Ch. 3.1 - In Exercises 29-32, find the mean of the data...Ch. 3.1 - In Exercises 29-32, find the mean of the data...Ch. 3.1 - Weighted Mean A student of the author earned...Ch. 3.1 - Weighted Mean A student of the author earned...Ch. 3.1 - Degrees of Freedom Five pulse rates randomly...Ch. 3.1 - Censored Data Data Set 15 Presidents in Appendix B...Ch. 3.1 - Trimmed Mean Because the mean is very sensitive to...Ch. 3.1 - Harmonic Mean The harmonic mean is often used as a...Ch. 3.1 - Geometric Mean The geometric mean is often used in...Ch. 3.1 - Quadratic Mean The quadratic mean (or root mean...Ch. 3.1 - Median When data are summarized in a frequency...Ch. 3.2 - Range Rule of Thumb for Estimating s The 20 brain...Ch. 3.2 - Range Rule of Thumb for Interpreting s The 20...Ch. 3.2 - Variance The 20 subjects used in Data Set 8 IQ and...Ch. 3.2 - Symbols Identify the symbols used for each of the...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 5-20, find the range, variance, and...Ch. 3.2 - In Exercises 21-24, find the coefficient of...Ch. 3.2 - In Exercises 21-24, find the coefficient of...Ch. 3.2 - In Exercises 21-24, find the coefficient of...Ch. 3.2 - In Exercises 21-24, find the coefficient of...Ch. 3.2 - Large Data Sets from Appendix B. In Exercises...Ch. 3.2 - Prob. 26BSCCh. 3.2 - Large Data Sets from Appendix B. In Exercises...Ch. 3.2 - Large Data Sets from Appendix B. In Exercises...Ch. 3.2 - Estimating Standard Deviation with the Range Rule...Ch. 3.2 - Prob. 30BSCCh. 3.2 - Estimating Standard Deviation with the Range Rule...Ch. 3.2 - Estimating Standard Deviation with the Range Rule...Ch. 3.2 - Identifying Significant Values with the Range Rule...Ch. 3.2 - Prob. 34BSCCh. 3.2 - Foot Lengths Based on Data Set 2 Foot and Height...Ch. 3.2 - Identifying Significant Values with the Range Rule...Ch. 3.2 - Finding Standard Deviation from a Frequency...Ch. 3.2 - Finding Standard Deviation from a Frequency...Ch. 3.2 - Finding Standard Deviation from a Frequency...Ch. 3.2 - Finding Standard Deviation from a Frequency...Ch. 3.2 - The Empirical Rule Based on Data Set 1 Body Data...Ch. 3.2 - The Empirical Rule Based on Data Set 3 Body...Ch. 3.2 - Chebyshevs Theorem Based on Data Set 1 Body Data...Ch. 3.2 - Chebyshevs Theorem Based on Data Set 3 Body...Ch. 3.2 - Why Divide by n 1? Let a population consist of...Ch. 3.2 - Mean Absolute Deviation Use the same population of...Ch. 3.3 - z Scores LeBron James, one of the most successful...Ch. 3.3 - Heights The boxplot shown below results from the...Ch. 3.3 - Boxplot Comparison Refer to the boxplots shown...Ch. 3.3 - z Scores If your score on your next statistics...Ch. 3.3 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.3 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.3 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.3 - z Scores. In Exercises 5-8, express all z scores...Ch. 3.3 - Significant Values. In Exercises 9-12, consider a...Ch. 3.3 - Significant Values. In Exercises 9-12, consider a...Ch. 3.3 - Significant Values. In Exercises 9-12, consider a...Ch. 3.3 - Significant Values. In Exercises 9-12, consider a...Ch. 3.3 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.3 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.3 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.3 - Comparing Values. In Exercises 13-16, use z scores...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Percentiles. In Exercises 17-20, use the following...Ch. 3.3 - Boxplots. In Exercises 29-32, use the given data...Ch. 3.3 - Boxplots. In Exercises 29-32, use the given data...Ch. 3.3 - Boxplots. In Exercises 29-32, use the given data...Ch. 3.3 - Boxplots. In Exercises 29-32, use the given data...Ch. 3.3 - Boxplots from Large Data Sets in Appendix B. In...Ch. 3.3 - Boxplots from Large Data Sets in Appendix B. In...Ch. 3.3 - Prob. 35BSCCh. 3.3 - Boxplots from Large Data Sets in Appendix B. In...Ch. 3.3 - Outliers and Modified Boxplots Repeat Exercise 33...Ch. 3 - Sleep Mean As part of the National Health and...Ch. 3 - Sleep Median What is the median of the sample...Ch. 3 - Sleep Mode What is the mode of the sample values...Ch. 3 - Sleep Variance The standard deviation of the...Ch. 3 - Prob. 5CQQCh. 3 - Sleep z Score A larger sample of 50 sleep times...Ch. 3 - Sleep Q3 For a sample of 80 sleep times,...Ch. 3 - Sleep 5-Number Summary For a sample of 100 sleep...Ch. 3 - Estimating s A large sample of sleep times...Ch. 3 - Sleep Notation Consider a sample of sleep times...Ch. 3 - Old Faithful Geyser Listed below are prediction...Ch. 3 - z Score Using the sample data from Exercise 1,...Ch. 3 - Boxplot Using the same prediction errors listed in...Ch. 3 - ER Codes In an analysis of activities that...Ch. 3 - Comparing Birth Weights The birth weights of a...Ch. 3 - Effects of an Outlier Listed below are platelet...Ch. 3 - Interpreting a Boxplot Shown below is a boxplot of...Ch. 3 - Estimating Standard Deviation Listed below is a...Ch. 3 - Prob. 1CRECh. 3 - Prob. 2CRECh. 3 - Stemplot Use the amounts of arsenic from Exercise...Ch. 3 - Prob. 4CRECh. 3 - Histogram The accompanying histogram depicts...Ch. 3 - Normal Distribution Examine the distribution shown...Ch. 3 - Words Spoken by Men and Women Refer to Data Set 24...Ch. 3 - Second-Hand Smoke Data Set 12 Passive and Active...
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- 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 I+I+I+I+Oooo 0 0 ||++TI++o000 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?arrow_forwardStem1: 1,4 Stem 2: 2,4,8 Stem3: 2,4 Stem4: 0,1,6,8 Stem5: 0,1,2,3,9 Stem 6: 2,2 What’s the Min,Q1, Med,Q3,Max?arrow_forwardAre the t-statistics here greater than 1.96? What do you conclude? colgPA= 1.39+0.412 hsGPA (.33) (0.094) Find the P valuearrow_forward
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