Elementary Statistics: Picturing the World (7th Edition)
7th Edition
ISBN: 9780134683744
Author: Larson
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 (7th Edition)
Ch. 6.1 - In Example 1, the researcher selects a second...Ch. 6.1 - Use the data in Try It Yourself 1 and a 95%...Ch. 6.1 - Use the data in Try It Yourself 1 to construct a...Ch. 6.1 - Use the data in Example 1 and technology to...Ch. 6.1 - Construct a 90% confidence interval for the...Ch. 6.1 - In Example 6, how many student-athletes must the...Ch. 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 - Finding the Margin of Error In Exercises 33 and...Ch. 6.1 - Constructing Confidence Intervals In Exercises...Ch. 6.1 - Constructing Confidence Intervals In Exercises...Ch. 6.1 - Constructing Confidence Intervals In Exercises...Ch. 6.1 - Constructing Confidence Intervals In Exercises...Ch. 6.1 - In Exercise 35, does it seem possible that the...Ch. 6.1 - In Exercise 36, does it seem possible that the...Ch. 6.1 - In Exercise 37, does it seem possible that the...Ch. 6.1 - In Exercise 38, does it seem possible that the...Ch. 6.1 - When all other quantities remain the same, how...Ch. 6.1 - Constructing Confidence Intervals In Exercises 45...Ch. 6.1 - Constructing Confidence Intervals In Exercises 45...Ch. 6.1 - Determining a Minimum Sample Size Determine the...Ch. 6.1 - Determining a Minimum Sample Size Determine the...Ch. 6.1 - Cholesterol Contents of Cheese A cheese processing...Ch. 6.1 - Ages of College Students An admissions director...Ch. 6.1 - Paint Can Volumes A paint manufacturer uses a...Ch. 6.1 - Juice Dispensing Machine A beverage company uses a...Ch. 6.1 - Soccer Balls A soccer ball manufacturer wants to...Ch. 6.1 - Tennis Balls A tennis ball manufacturer wants to...Ch. 6.1 - When estimating the population mean, why not...Ch. 6.1 - When all other quantities remain the same, how...Ch. 6.1 - Determine the finite population coection factor...Ch. 6.1 - Use the finite population correction factor to...Ch. 6.1 - Sample Size The equation for determining the...Ch. 6.2 - Find the critical value tc for a 90% confidence...Ch. 6.2 - Construct 90% and 99% confidence intervals for the...Ch. 6.2 - Construct 90% and 95% confidence intervals for the...Ch. 6.2 - You randomly select 18 adult male athletes and...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 - 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 - Constructing a Confidence Interval In Exercises...Ch. 6.2 - Constructing a Confidence Interval In Exercises...Ch. 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 - You research prices of cell phones and find that...Ch. 6.2 - You research repair costs of mobile devices and...Ch. 6.2 - Constructing a Confidence Interval in Exercises...Ch. 6.2 - Constructing a Confidence Interval in Exercises...Ch. 6.2 - Constructing a Confidence Interval in Exercises...Ch. 6.2 - Constructing a Confidence Interval in Exercises...Ch. 6.2 - In Exercise 25, the population mean SAT score is...Ch. 6.2 - In Exercise 28, the population mean weekly time...Ch. 6.2 - Constructing a Confidence Interval Ir. Exercises...Ch. 6.2 - Constructing a Confidence Interval Ir. Exercises...Ch. 6.2 - In Exercise 31, the population mean salary is...Ch. 6.2 - In Exercise 32, the population mean salary is...Ch. 6.2 - Choosing a Distribution In Exercises 3538, use the...Ch. 6.2 - Choosing a Distribution In Exercises 3538, use the...Ch. 6.2 - Choosing a Distribution In Exercises 3538, use the...Ch. 6.2 - Choosing a Distribution In Exercises 3538, use the...Ch. 6.2 - In Exercise 36, does it seem possible that the...Ch. 6.2 - In Exercise 38, does it seem possible that the...Ch. 6.2 - Tennis Ball Manufacturing A company manufactures...Ch. 6.2 - Light Bulb Manufacturing A company manufactures...Ch. 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 - A poll surveyed 4780 U.S. adults about how often...Ch. 6.3 - Use the data in Try It Yourself 1 to construct a...Ch. 6.3 - Use the data in Example 3 to construct a 99%...Ch. 6.3 - A researcher is estimating the population...Ch. 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 - Finding p and q In Exercises 36, let p be the...Ch. 6.3 - Finding p and q In Exercises 36, let p be the...Ch. 6.3 - Finding p and q In Exercises 36, let p be the...Ch. 6.3 - Finding p and q In Exercises 36, let p be the...Ch. 6.3 - In Exercises 710, use the confidence interval to...Ch. 6.3 - In Exercises 710, use the confidence interval to...Ch. 6.3 - In Exercises 710, use the confidence interval to...Ch. 6.3 - In Exercises 710, use the confidence interval to...Ch. 6.3 - Constructing Confidence Intervals In Exercises 11...Ch. 6.3 - Constructing Confidence Intervals In Exercises 11...Ch. 6.3 - Constructing Confidence Intervals In Exercises 13...Ch. 6.3 - Constructing Confidence Intervals In Exercises 13...Ch. 6.3 - LGBT Identification In a survey of 1,626,773 U.S....Ch. 6.3 - Transgender Bathroom Policy In a survey of 1000...Ch. 6.3 - Congress You wish to estimate, with 95%...Ch. 6.3 - Genetically Modified Organisms You wish to...Ch. 6.3 - Fast Food You wish to estimate, with 90%...Ch. 6.3 - Alcohol-Impaired Driving You wish to estimate,...Ch. 6.3 - In Exercise 11, does it seem possible that the...Ch. 6.3 - In Exercise 14, does it seem possible that the...Ch. 6.3 - In Exercise 17(b), would a sample size of 200 be...Ch. 6.3 - In Exercise 20(b), would a sample size of 600 be...Ch. 6.3 - Constructing Confidence Intervals In Exercises 25...Ch. 6.3 - Constructing Confidence Intervals In Exercises 25...Ch. 6.3 - Constructing Confidence Intervals In Exercises 27...Ch. 6.3 - Constructing Confidence Intervals In Exercises 27...Ch. 6.3 - Translating Statements In Exercises 2934,...Ch. 6.3 - Translating Statements In Exercises 2934,...Ch. 6.3 - Prob. 31ECh. 6.3 - Translating Statements In Exercises 2934,...Ch. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 1ACh. 6.3 - Prob. 2ACh. 6.4 - Kind the critical values R2 and I2 for a 90%...Ch. 6.4 - Construct the 90% and 95% confidence intervals for...Ch. 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 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 6.4 - Constructing Confidence Intervals In Exercises...Ch. 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. 6.4 - Prob. 28ECh. 6.4 - Prob. 29ECh. 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 - In Exercises 19-22, let p be the population...Ch. 6 - Prob. 6.3.20RECh. 6 - In Exercises 19-22, let p be the population...Ch. 6 - Prob. 6.3.22RECh. 6 - In Exercise 19, does it seem possible that the...Ch. 6 - Prob. 6.3.24RECh. 6 - Prob. 6.3.25RECh. 6 - Prob. 6.3.26RECh. 6 - Prob. 6.4.27RECh. 6 - Prob. 6.4.28RECh. 6 - Prob. 6.4.29RECh. 6 - In Exercises 2730, find the critical values R2 and...Ch. 6 - Prob. 6.4.31RECh. 6 - In Exercises 31 and 32, assume the sample is from...Ch. 6 - The winning times (in hours) for a sample of 30...Ch. 6 - The data set represents the amounts of time (in...Ch. 6 - Prob. 4CQCh. 6 - Prob. 5CQCh. 6 - Prob. 6CQCh. 6 - Refer to the data set in Exercise 3. Assume the...Ch. 6 - In a survey of 20% U.S. adults, 1740 think...Ch. 6 - The data set represents the weights (in pounds) of...Ch. 6 - The data set represents the scores of 12 randomly...Ch. 6 - Use the standard normal distribution or the...Ch. 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 - Since 1935, the Gallup Organization has conducted...Ch. 6 - THE GALLUP ORGANIZATION www.gallup.com Since 1935,...Ch. 6 - Since 1935, the Gallup Organization has conducted...Ch. 6 - Since 1935, the Gallup Organization has conducted...
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