Understanding Basic Statistics
8th Edition
ISBN: 9781337672320
Author: BRASE
Publisher: Cengage
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Textbook Question
Chapter 2, Problem 4CR
Terminology Which graphical display shows each data value (or truncated data value) in order from smallest to largest: histogram, pie chart, stem-and-leaf?
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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 2 Solutions
Understanding Basic Statistics
Ch. 2.1 - Statistical Literacy What is the difference...Ch. 2.1 - Statistical Literacy A data set has values ranging...Ch. 2.1 - Statistical Literacy A data set has values ranging...Ch. 2.1 - Statistical Literacy A data set has value ranging...Ch. 2.1 - Basic Computation: Class Limits A data set with...Ch. 2.1 - Basic Computation: Class limits A data set with...Ch. 2.1 - Interpretation You are manager of a specialty...Ch. 2.1 - Critical Thinking A web site rated 100 colleges...Ch. 2.1 - Critical Thinking Look at the histogram in Figure...Ch. 2.1 - Critical Thinking The following data represent...
Ch. 2.1 - Interpretation Histograms of random sample data...Ch. 2.1 - Interpretation The following histograms are based...Ch. 2.1 - Interpretation The ogives shown are based on U.S...Ch. 2.1 - Critical Thinking The following ogives come from...Ch. 2.1 - For Problems 15-20. use the specified number of...Ch. 2.1 - For Problems 15-20, use the specified number of...Ch. 2.1 - For Problems 15-20, use the specified number of...Ch. 2.1 - For Problems 15-20, use the specified number of...Ch. 2.1 - For Problems 15-20, use the specified number of...Ch. 2.1 - For Problems 15-20. use the specified number of...Ch. 2.1 - Expand Your knowledge: Decimal Data The fallowing...Ch. 2.1 - Decimal Data: Batting Averages The following data...Ch. 2.1 - Expand Your Knowledge: Dotplot another display...Ch. 2.1 - 24. Dotplot: Sled Dog Racing Make a dotplot for...Ch. 2.1 - Prob. 25PCh. 2.2 - 1. Interpretation Consider graph (a) of Reasons...Ch. 2.2 - Interpretation Look at graph (b) of Reasons People...Ch. 2.2 - Critical Thinking A personnel office is gathering...Ch. 2.2 - Critical Thinking Your friend is thinking about...Ch. 2.2 - Education: Does College Pay Off? It is costly in...Ch. 2.2 - Interpretation Consider the two graphs depicting...Ch. 2.2 - Commercial Fishing: Gulf of Alaska It's not an...Ch. 2.2 - Archaeology: Ireland Commercial dredging...Ch. 2.2 - Lifestyle: Hide the Mess! A survey of 1000 adults...Ch. 2.2 - Education: College Professors' Time How do college...Ch. 2.2 - FBI Report: Hawaii In the Aloha state, you are...Ch. 2.2 - Driving: Bad Habits Driving would be more pleasant...Ch. 2.2 - 13Ecology: Lakes Pyramid Lake, Nevada, is...Ch. 2.2 - Vital Statistics: Height How dies average height...Ch. 2.2 - Expand Your Knowledge Donut Pie Charts The book...Ch. 2.2 - Technology: Cars The following cluster bar graph...Ch. 2.3 - Cowboys: Longevity How long did real cowboys live?...Ch. 2.3 - Ecology: Habitat Wetlands offer a diversity of...Ch. 2.3 - Health Care: Hospitals The American Medical...Ch. 2.3 - Health Care: Hospitals Using the number of...Ch. 2.3 - Expand Your knowledge: Split Stem The Boston...Ch. 2.3 - Split Stem: Golf The U.S. Open Golf Tournament was...Ch. 2.3 - Are cigarettes bad for people? Cigarette smoking...Ch. 2.3 - Are cigarettes bad for people? Cigarette smoking...Ch. 2.3 - Are cigarettes bad for people? Cigarette smoking...Ch. 2.3 - Expand Your Knowledge: Back-to-Back Stem Plot In...Ch. 2 - Terminology Consider the following graph types:...Ch. 2 - Terminology Whichtype(s) of data can be shown in a...Ch. 2 - Terminology Which type(s) of data can be shown in...Ch. 2 - Terminology Which graphical display shows each...Ch. 2 - Terminology If a histogram is skewed left, more of...Ch. 2 - Terminology How are data plotted in a time-series...Ch. 2 - Critical Thinking Consider these types of graphs:...Ch. 2 - Critical Thinking A consumer interest group is...Ch. 2 - Critical Thinking Describe how data outliers might...Ch. 2 - Expand Your Knowledge How are dotplots and...Ch. 2 - Focus Problem: Fuel Economy Solve the focus...Ch. 2 - Criminal Justice: Prisoners The time plot in...Ch. 2 - IRS: Tax Returns Almost everyone files (or will...Ch. 2 - Law Enforcement: DUI Driving under the influence...Ch. 2 - Agriculture: Apple Trees The following data...Ch. 2 - Law: Corporation Lawsuits Many people say the...Ch. 2 - Archaeology: Tree-King DataThe Sand Canyon...Ch. 2 - Interpretation A Harm Poll surveyed 2085 U.S....Ch. 2 - Examine Figure 2-20, Everyone Agrees: Slobs Make...Ch. 2 - Examine Figure 2-21, Global Teen Worries. How many...Ch. 2 - In your own words, explain the differences among...Ch. 2 - What do we mean when we say a histogram is skewed...Ch. 2 - Discuss the statement that stem-and-leaf displays...Ch. 2 - The following tables show the first-round winning...Ch. 2 - The following tables show the first-round winning...Ch. 2 - The Following tables show the first-round winning...
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