Elementary Statistics: Picturing the World (6th Edition)
6th Edition
ISBN: 9780321911216
Author: Ron Larson, Betsy Farber
Publisher: PEARSON
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Chapter 6.4, Problem 5E
To determine
To find: The critical values
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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 6 Solutions
Elementary Statistics: Picturing the World (6th Edition)
Ch. 6.1 - Prob. 1TYCh. 6.1 - Prob. 2TYCh. 6.1 - Prob. 3TYCh. 6.1 - Prob. 4TYCh. 6.1 - Prob. 5TYCh. 6.1 - Prob. 6TYCh. 6.1 - When estimating a population mean, are you more...Ch. 6.1 - Which statistic is the best unbiased estimator for...Ch. 6.1 - For the same sample statistics, which level of...Ch. 6.1 - You construct a 95% confidence interval for a...
Ch. 6.1 - In Exercises 58, find the critical value Zc...Ch. 6.1 - In Exercises 58, find the critical value Zc...Ch. 6.1 - In Exercises 58, find the critical value Zc...Ch. 6.1 - In Exercises 58, find the critical value Zc...Ch. 6.1 - Graphical Analysis In Exercises 912, use the...Ch. 6.1 - Graphical Analysis In Exercises 912, use the...Ch. 6.1 - Graphical Analysis In Exercises 912, use the...Ch. 6.1 - Graphical Analysis In Exercises 912, use the...Ch. 6.1 - In Exercises 1316, find the margin of error for...Ch. 6.1 - In Exercises 1316, find the margin of error for...Ch. 6.1 - In Exercises 1316, find the margin of error for...Ch. 6.1 - In Exercises 1316, find the margin of error for...Ch. 6.1 - Matching In Exercises 1720, match the level of...Ch. 6.1 - Matching In Exercises 1720, match the level of...Ch. 6.1 - Matching In Exercises 1720, match the level of...Ch. 6.1 - Matching In Exercises 1720, match the level of...Ch. 6.1 - In Exercises 2124, construct the indicated...Ch. 6.1 - In Exercises 2124, construct the indicated...Ch. 6.1 - In Exercises 2124, construct the indicated...Ch. 6.1 - In Exercises 2124, construct the indicated...Ch. 6.1 - In Exercises 2528, use the confidence interval to...Ch. 6.1 - In Exercises 2528, use the confidence interval to...Ch. 6.1 - In Exercises 2528, use the confidence interval to...Ch. 6.1 - In Exercises 2528, use the confidence interval to...Ch. 6.1 - In Exercises 2932, determine the minimum sample...Ch. 6.1 - In Exercises 2932, determine the minimum sample...Ch. 6.1 - In Exercises 2932, determine the minimum sample...Ch. 6.1 - In Exercises 2932, determine the minimum sample...Ch. 6.1 - Finding the Margin of Error In Exercises 33 and...Ch. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Prob. 37ECh. 6.1 - Prob. 38ECh. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Prob. 42ECh. 6.1 - When all other quantities remain the same, how...Ch. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Determining a Minimum Sample Size Determine the...Ch. 6.1 - Determining a Minimum Sample Size Determine the...Ch. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - Prob. 53ECh. 6.1 - Prob. 54ECh. 6.1 - When all other quantities remain the same, how...Ch. 6.1 - When estimating the population mean, why not...Ch. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - Use the finite population correction factor to...Ch. 6.1 - Sample Size The equation for determining the...Ch. 6.2 - Prob. 1TYCh. 6.2 - Prob. 2TYCh. 6.2 - Prob. 3TYCh. 6.2 - Prob. 4TYCh. 6.2 - Finding Critical Values of t In Exercises 14, find...Ch. 6.2 - Finding Critical Values of t In Exercises 14, find...Ch. 6.2 - Finding Critical Values of t In Exercises 14, find...Ch. 6.2 - Finding Critical Values of t In Exercises 14, find...Ch. 6.2 - In Exercises 58, find the margin of error for the...Ch. 6.2 - In Exercises 58, find the margin of error for the...Ch. 6.2 - In Exercises 58, find the margin of error for the...Ch. 6.2 - In Exercises 58, find the margin of error for the...Ch. 6.2 - In Exercises 912, construct the indicated...Ch. 6.2 - In Exercises 912, construct the indicated...Ch. 6.2 - In Exercises 912, construct the indicated...Ch. 6.2 - In Exercises 912, construct the indicated...Ch. 6.2 - In Exercises 1316, use the confidence interval to...Ch. 6.2 - In Exercises 1316, use the confidence interval to...Ch. 6.2 - In Exercises 1316, use the confidence interval to...Ch. 6.2 - In Exercises 1316, use the confidence interval to...Ch. 6.2 - Constructing a Confidence Interval In Exercises...Ch. 6.2 - Constructing a Confidence Interval In Exercises...Ch. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.2 - You research commute times to work and find that...Ch. 6.2 - You research driving distances to work and find...Ch. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Constructing a Confidence Interval in Exercises...Ch. 6.2 - Constructing a Confidence Interval in Exercises...Ch. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Choosing a Distribution In Exercises 3538, use the...Ch. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 1ACh. 6.2 - In a random sample of 24 high school students, the...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.2 - A marathon is a fool race with a distance of 26.22...Ch. 6.3 - Prob. 1TYCh. 6.3 - Prob. 2TYCh. 6.3 - Prob. 3TYCh. 6.3 - Prob. 4TYCh. 6.3 - True or False? In Exercises 1 and 2, determine...Ch. 6.3 - True or False? In Exercises 1 and 2, determine...Ch. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - Prob. 11ECh. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.3 - Prob. 20ECh. 6.3 - Prob. 21ECh. 6.3 - Prob. 22ECh. 6.3 - Prob. 23ECh. 6.3 - Prob. 24ECh. 6.3 - Prob. 25ECh. 6.3 - Prob. 26ECh. 6.3 - Prob. 27ECh. 6.3 - Prob. 28ECh. 6.3 - Prob. 29ECh. 6.3 - Prob. 30ECh. 6.3 - Prob. 31ECh. 6.3 - Prob. 1ACh. 6.3 - Prob. 2ACh. 6.4 - Prob. 1TYCh. 6.4 - Prob. 2TYCh. 6.4 - Does a population have to be normally distributed...Ch. 6.4 - What happens to the shape of the chi-square...Ch. 6.4 - Prob. 3ECh. 6.4 - Finding Critical Values for X2 In Exercises 38,...Ch. 6.4 - Prob. 5ECh. 6.4 - Finding Critical Values for X2 In Exercises 38,...Ch. 6.4 - Finding Critical Values for X2 In Exercises 38,...Ch. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - In Exercises 912, construct the indicated...Ch. 6.4 - Prob. 13ECh. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Prob. 21ECh. 6.4 - Prob. 22ECh. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Prob. 27ECh. 6 - The waking times (in minutes past 5:00 A.M.) of 40...Ch. 6 - The driving distances (in miles) to work of 30...Ch. 6 - Prob. 6.1.3RECh. 6 - Prob. 6.1.4RECh. 6 - In Exercises 5 and 6, use the confidence interval...Ch. 6 - Prob. 6.1.6RECh. 6 - Prob. 6.1.7RECh. 6 - Prob. 6.1.8RECh. 6 - In Exercises 912, find the critical value tc for...Ch. 6 - In Exercises 912, find the critical value tc for...Ch. 6 - In Exercises 912, find the critical value tc for...Ch. 6 - Prob. 6.2.12RECh. 6 - Prob. 6.2.13RECh. 6 - Prob. 6.2.14RECh. 6 - Prob. 6.2.15RECh. 6 - Prob. 6.2.16RECh. 6 - Prob. 6.2.17RECh. 6 - Prob. 6.2.18RECh. 6 - Prob. 6.2.19RECh. 6 - Prob. 6.2.20RECh. 6 - Prob. 6.2.21RECh. 6 - Prob. 6.2.22RECh. 6 - Prob. 6.3.23RECh. 6 - Prob. 6.3.24RECh. 6 - Prob. 6.3.25RECh. 6 - Prob. 6.3.26RECh. 6 - Prob. 6.3.27RECh. 6 - Prob. 6.3.28RECh. 6 - Prob. 6.3.29RECh. 6 - Prob. 6.3.30RECh. 6 - Prob. 6.3.31RECh. 6 - Prob. 6.3.32RECh. 6 - Prob. 6.4.33RECh. 6 - Prob. 6.4.34RECh. 6 - Prob. 6.4.35RECh. 6 - In Exercises 2730, find the critical values R2 and...Ch. 6 - Prob. 6.4.37RECh. 6 - Prob. 6.4.38RECh. 6 - Prob. 1CQCh. 6 - Prob. 2CQCh. 6 - The data set represents the amounts of time (in...Ch. 6 - Prob. 4CQCh. 6 - Prob. 5CQCh. 6 - Prob. 6CQCh. 6 - Prob. 1CTCh. 6 - Prob. 2CTCh. 6 - Prob. 3CTCh. 6 - Use the standard normal distribution or the...Ch. 6 - Prob. 5CTCh. 6 - The Safe Drinking Water Act, which was passed in...Ch. 6 - The Safe Drinking Water Act, which was passed in...Ch. 6 - The Safe Drinking Water Act, which was passed in...Ch. 6 - Prob. 4RSRDCh. 6 - Prob. 1TCh. 6 - Prob. 2TCh. 6 - Prob. 3TCh. 6 - Prob. 4TCh. 6 - Prob. 5T
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