ELEMENTARY STATISTICS: STEP BY STEP- ALE
10th Edition
ISBN: 9781266422362
Author: Bluman
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Chapter 14, Problem 3DA
Select a cluster sample of 20 individuals, and using the same variable as in Exercise 1, find the
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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 14 Solutions
ELEMENTARY STATISTICS: STEP BY STEP- ALE
Ch. 14.1 - The White or Wheat Bread Debate Read the following...Ch. 14.1 - Name the four basic sampling techniques.Ch. 14.1 - Why are samples used in statistics?Ch. 14.1 - What is the basic requirement for a sample?Ch. 14.1 - Why should random numbers be used when you are...Ch. 14.1 - List three incorrect methods that are often used...Ch. 14.1 - What is the principle behind random numbers?Ch. 14.1 - List the advantages and disadvantages of random...Ch. 14.1 - List the advantages and disadvantages of...Ch. 14.1 - List the advantages and disadvantages of...
Ch. 14.1 - List the advantages and disadvantages of cluster...Ch. 14.1 - Teacher Data Using the table of random numbers,...Ch. 14.1 - Prob. 12ECh. 14.1 - Teacher Data Select a cluster sample of 10 states,...Ch. 14.1 - Record High Temperatures Which method of sampling...Ch. 14.1 - Prob. 16ECh. 14.1 - Electoral Votes Select a systematic sample of 10...Ch. 14.1 - Electoral Votes Divide the 50 states into five...Ch. 14.1 - Prob. 19ECh. 14.1 - Define sampling or selection bias.Ch. 14.1 - Prob. 22ECh. 14.1 - Define nonresponsive bias.Ch. 14.1 - Prob. 24ECh. 14.1 - Define response or interview bias.Ch. 14.1 - Prob. 26ECh. 14.1 - Define volunteer bias.Ch. 14.1 - Give an example of how volunteer bias might occur.Ch. 14.2 - Prob. 1ACCh. 14.2 - Prob. 1ECh. 14.2 - Prob. 2ECh. 14.2 - Prob. 3ECh. 14.2 - Prob. 4ECh. 14.2 - Prob. 5ECh. 14.2 - Prob. 6ECh. 14.2 - Prob. 7ECh. 14.2 - Prob. 8ECh. 14.2 - Prob. 9ECh. 14.2 - Exercises 1 through 9 include questions that...Ch. 14.2 - Prob. 11ECh. 14.2 - Exercises 1 through 9 include questions that...Ch. 14.2 - Prob. 13ECh. 14.2 - Prob. 14ECh. 14.2 - Prob. 15ECh. 14.2 - Exercises 1 through 9 include questions that...Ch. 14.2 - Prob. 17ECh. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.3 - Simulations Answer the following questions: 1....Ch. 14.3 - Prob. 1ECh. 14.3 - Prob. 2ECh. 14.3 - Who is responsible for the development of modern...Ch. 14.3 - Prob. 4ECh. 14.3 - Prob. 5ECh. 14.3 - Prob. 6ECh. 14.3 - Prob. 7ECh. 14.3 - Prob. 8ECh. 14 - Hurricanes Select a random sample of eight storms...Ch. 14 - Prob. 14.1.2RECh. 14 - Hurricanes Select a cluster of 10 storms. Compute...Ch. 14 - Prob. 14.1.4RECh. 14 - Prob. 14.1.5RECh. 14 - Prob. 14.1.6RECh. 14 - Prob. 14.1.8RECh. 14 - Prob. 14.2.9RECh. 14 - Prob. 14.2.10RECh. 14 - Prob. 14.2.11RECh. 14 - Prob. 14.2.12RECh. 14 - Prob. 1DACh. 14 - Prob. 2DACh. 14 - Select a cluster sample of 20 individuals, and...Ch. 14 - Prob. 4DACh. 14 - Prob. 5DACh. 14 - Determine whether each statement is true or false....Ch. 14 - Prob. 2CQCh. 14 - Prob. 3CQCh. 14 - Prob. 4CQCh. 14 - Prob. 5CQCh. 14 - Prob. 6CQCh. 14 - Interviewing selected people at a local...Ch. 14 - Prob. 8CQCh. 14 - Prob. 9CQCh. 14 - Prob. 10CQCh. 14 - Blood Pressure Select a random sample of 12...Ch. 14 - Prob. 12CQCh. 14 - Blood Pressure Divide the individuals into...Ch. 14 - Prob. 14CQCh. 14 - Prob. 25CQCh. 14 - Prob. 26CQCh. 14 - Prob. 27CQCh. 14 - Prob. 28CQCh. 14 - For Exercises 2530, explain why the survey...Ch. 14 - Prob. 30CQCh. 14 - Prob. 1DP
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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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