Statistics, Books a la Carte Edition Plus MyLab Statistics with Pearson eText -- Access Card Package (4th Edition)
4th Edition
ISBN: 9780134435855
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
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Chapter 3.3, Problem 28PB
To determine
Identify the most accurate predictions for the cost of a dinner.
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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
Statistics, Books a la Carte Edition Plus MyLab Statistics with Pearson eText -- Access Card Package (4th Edition)
Ch. 3.1 - Which is the response/explanatory variable? For...Ch. 3.1 - Sales and advertising Each month, the owner of...Ch. 3.1 - Does higher income make you happy? Every General...Ch. 3.1 - Diamonds The clarity and cut of a diamond are two...Ch. 3.1 - Alcohol and college students The Harvard School of...Ch. 3.1 - How to fight terrorism? A survey of 1000 adult...Ch. 3.1 - Heaven and hell Two questions on the General...Ch. 3.1 - Prob. 8PBCh. 3.1 - Gender gap in party ID In recent election years,...Ch. 3.1 - Use the GSS Go to the GSS website...
Ch. 3.2 - Used cars and direction of association For the 100...Ch. 3.2 - Broadband and GDP The Internet Use data file on...Ch. 3.2 - Prob. 13PBCh. 3.2 - Politics and newspaper reading For the FL Student...Ch. 3.2 - Prob. 15PBCh. 3.2 - Match the scatterplot with r Match the following...Ch. 3.2 - Prob. 17PBCh. 3.2 - Prob. 18PBCh. 3.2 - Prob. 19PBCh. 3.2 - Prob. 20PBCh. 3.2 - Prob. 21PBCh. 3.2 - Prob. 22PBCh. 3.2 - Prob. 23PBCh. 3.3 - Sketch plots of lines Identify the values of the...Ch. 3.3 - Prob. 25PBCh. 3.3 - Home selling prices The House Selling Prices FL...Ch. 3.3 - Prob. 27PBCh. 3.3 - Prob. 28PBCh. 3.3 - Prob. 29PBCh. 3.3 - Broadband subscribers and population The Internet...Ch. 3.3 - Prob. 31PBCh. 3.3 - Prob. 32PBCh. 3.3 - Regression between cereal sodium and sugar The...Ch. 3.3 - Prob. 34PBCh. 3.3 - Advertising and sales Each month, the owner of...Ch. 3.3 - Midtermfinal correlation For students who take...Ch. 3.3 - Predict final exam from midterm In an introductory...Ch. 3.3 - NL baseball Example 9 related y = team scoring...Ch. 3.3 - Study time and college GPA A graduate teaching...Ch. 3.3 - Oil and GDP An article in the September 16, 2006,...Ch. 3.3 - Mountain bikes revisited Is there a relationship...Ch. 3.3 - Mountain bike and suspension type Refer to the...Ch. 3.3 - Fuel Consumption Most cars are fuel efficient when...Ch. 3.4 - Extrapolating murder The SPSS figure shows the...Ch. 3.4 - Mens Olympic long jumps The Olympic winning mens...Ch. 3.4 - U.S. average annual temperatures Use the U.S....Ch. 3.4 - Murder and education Example 13 found the...Ch. 3.4 - Murder and poverty For Table 3.6, the regression...Ch. 3.4 - TV watching and the birth rate The figure shows...Ch. 3.4 - Looking for outliers Using software, analyze the...Ch. 3.4 - Regression between cereal sodium and sugar Let x =...Ch. 3.4 - Gestational period and life expectancy Does the...Ch. 3.4 - Antidrug campaigns An Associated Press story (June...Ch. 3.4 - Whats wrong with regression? Explain whats wrong...Ch. 3.4 - Education causes crime? The table shows a small...Ch. 3.4 - Death penalty and race The table shows results of...Ch. 3.4 - NAEP scores Eighth-grade math scores on the...Ch. 3.4 - Age a confounder? A study observes that the...Ch. 3 - Choose explanatory and response For the following...Ch. 3 - Graphing data For each case in the previous...Ch. 3 - Life after death for males and females In a recent...Ch. 3 - God and happiness Go to the GSS website...Ch. 3 - Degrees and income The mean annual salaries earned...Ch. 3 - Bacteria in ground turkey Consumer Reports...Ch. 3 - Women managers in the work force The following...Ch. 3 - RateMyProfessor.com The website RateMyProfessors....Ch. 3 - Women in government and economic life The OECD...Ch. 3 - African droughts and dust Is there a relationship...Ch. 3 - Crime rate and urbanization For the data in...Ch. 3 - Gestational period and life expectancy revisited...Ch. 3 - Height and paycheck The headline of an article in...Ch. 3 - Predicting college GPA An admissions officer...Ch. 3 - College GPA = high school GPA Refer to the...Ch. 3 - Whats a college degree worth? In 2002, a census...Ch. 3 - Care Weight and gas hogs: The table shows a short...Ch. 3 - Predicting Internet use from cell phone use We now...Ch. 3 - Income depends on education? For a study of...Ch. 3 - Fertility and GDP Refer to the Human Development...Ch. 3 - Women working and birth rate Using data from...Ch. 3 - Education and income The regression equation for a...Ch. 3 - Income in euros Refer to the previous exercise....Ch. 3 - Changing units for cereal data Refer to the Cereal...Ch. 3 - Murder and single-parent families For Table 3.6 on...Ch. 3 - Violent crime and college education For the U.S....Ch. 3 - Violent crime and high school education Repeat the...Ch. 3 - Crime and urbanization For the U.S. Statewide...Ch. 3 - High school graduation rates and health insurance...Ch. 3 - Womens Olympic high jumps Example 11 discussed how...Ch. 3 - Income and height A survey of adults revealed a...Ch. 3 - More TV watching goes with fewer babies? For...Ch. 3 - More sleep causes death? An Associated Press story...Ch. 3 - Ask Marilyn Marilyn vos Savant writes a column for...Ch. 3 - Time studying and GPA Is there a relationship...Ch. 3 - Warming in Newnan, Georgia Access the Newnan GA...Ch. 3 - Fluoride and AIDS An Associated Press story...Ch. 3 - Fish fights Alzheimers An AP story (July 22, 2003)...Ch. 3 - Dogs make you healthier A study published in the...Ch. 3 - Multiple choice: Correlate GPA and GRE In a study...Ch. 3 - Multiple choice: Properties of r Which of the...Ch. 3 - Multiple choice: Interpreting r One can interpret...Ch. 3 - Multiple choice: Correct statement about r Which...Ch. 3 - Multiple choice: Describing association between...Ch. 3 - Multiple choice: Slope and correlation The slope...Ch. 3 - Multiple choice: Interpretation of r2 An r2...Ch. 3 - True or false The variables y = annual income...Ch. 3 - Correlation doesnt depend on units Suppose you...Ch. 3 - When correlation = slope Consider the formula...Ch. 3 - Center of the data Consider the formula a=ybx for...Ch. 3 - Final exam regresses toward mean of midterm Let y...Ch. 3 - Activity: Guess the correlation The Guess the...
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