Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
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Chapter 1.1, Problem 25E
To determine
Identify the kind of sample drawn.
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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 1 Solutions
Essential Statistics
Ch. 1.1 - 1. A pollster wants to estimate the proportion of...Ch. 1.1 - Prob. 2CYUCh. 1.1 - 3. A radio talk-show host invites listeners to...Ch. 1.1 - 4. Every 10 years, the U.S. Census Bureau attempts...Ch. 1.1 - 5. A public health researcher is designing a study...Ch. 1.1 - 6. A college basketball team held a promotion at...Ch. 1.1 - Prob. 7ECh. 1.1 - In Exercises 7–12, fill in each blank with the...Ch. 1.1 - In Exercises 7–12, fill in each blank with the...Ch. 1.1 - In Exercises 7–12, fill in each blank with the...
Ch. 1.1 - In Exercises 7–12, fill in each blank with the...Ch. 1.1 - In Exercises 7–12, fill in each blank with the...Ch. 1.1 - In Exercises 13–16, determine whether the...Ch. 1.1 - In Exercises 13–16, determine whether the...Ch. 1.1 - In Exercises 13–16, determine whether the...Ch. 1.1 - In Exercises 13–16, determine whether the...Ch. 1.1 - Prob. 17ECh. 1.1 - In Exercises 17–20, determine whether the number...Ch. 1.1 - Prob. 19ECh. 1.1 - In Exercises 17–20, determine whether the number...Ch. 1.1 - Prob. 21ECh. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - Prob. 25ECh. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - In Exercises 25–36, identify the kind of sample...Ch. 1.1 - 39. You’re giving me a headache: A pharmaceutical...Ch. 1.1 - 40. Pay more for recreation? The director of the...Ch. 1.1 - Prob. 41ECh. 1.1 - 42. Quality control: Products come off an assembly...Ch. 1.1 - 43. On-site day care: A large company wants to...Ch. 1.1 - Prob. 44ECh. 1.1 - 45. Draw a sample: Imagine that you are asked to...Ch. 1.1 - Prob. 46ECh. 1.2 - 1. A pollster asks a group of six voters about...Ch. 1.2 - Prob. 2CYUCh. 1.2 - Prob. 3CYUCh. 1.2 - Prob. 4CYUCh. 1.2 - Prob. 5ECh. 1.2 - Prob. 6ECh. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - Prob. 10ECh. 1.2 - Prob. 11ECh. 1.2 - In Exercises 11–14, determine whether the...Ch. 1.2 - In Exercises 11–14, determine whether the...Ch. 1.2 - In Exercises 11–14, determine whether the...Ch. 1.2 - Prob. 15ECh. 1.2 - In Exercises 15–24, determine whether the data...Ch. 1.2 - Prob. 17ECh. 1.2 - In Exercises 15–24, determine whether the data...Ch. 1.2 - In Exercises 15–24, determine whether the data...Ch. 1.2 - In Exercises 15–24, determine whether the data...Ch. 1.2 - Prob. 21ECh. 1.2 - In Exercises 15–24, determine whether the data...Ch. 1.2 - Prob. 23ECh. 1.2 - In Exercises 15–24, determine whether the data...Ch. 1.2 - Prob. 25ECh. 1.2 - In Exercises 25–32, determine whether the data...Ch. 1.2 - Prob. 27ECh. 1.2 - In Exercises 25–32, determine whether the data...Ch. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - In Exercises 25–32, determine whether the data...Ch. 1.2 - Prob. 33ECh. 1.2 - In Exercises 33–40, determine whether the data...Ch. 1.2 - Prob. 35ECh. 1.2 - In Exercises 33–40, determine whether the data...Ch. 1.2 - Prob. 37ECh. 1.2 - In Exercises 33–40, determine whether the data...Ch. 1.2 - Prob. 39ECh. 1.2 - In Exercises 33–40, determine whether the data...Ch. 1.2 - Working with the Concepts
41. Ringtones: Following...Ch. 1.2 - 42. More Ringtones: The following table presents...Ch. 1.2 - 43. How’s the economy? A poll conducted by the...Ch. 1.2 - 44. Global warming: A recent Pew poll asked people...Ch. 1.2 - 45. Read any good books lately? According to Time...Ch. 1.2 - 46. Watch your language: According to...Ch. 1.2 - 47. Top ten PC games: Nielsen Media recently...Ch. 1.2 - 48. At the movies: The following table provides...Ch. 1.2 - Prob. 49ECh. 1.3 - 1. To study the effect of air pollution on...Ch. 1.3 - 2. It is known that drinking alcohol increases the...Ch. 1.3 - In a study conducted at the University of Southern...Ch. 1.3 - In a study conducted at the University of...Ch. 1.3 - In Exercises 5–10, fill in each blank with the...Ch. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - Prob. 9ECh. 1.3 - Prob. 10ECh. 1.3 - Prob. 11ECh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - In Exercises 11–16, determine whether the...Ch. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - 23. Taxicabs and crime: A sociologist discovered...Ch. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.3 - Prob. 29ECh. 1.3 - Prob. 30ECh. 1.4 - Exercises 1 and 2 are the Check Your Understanding...Ch. 1.4 - Exercises 1 and 2 are the Check Your Understanding...Ch. 1.4 - Prob. 3ECh. 1.4 - Prob. 4ECh. 1.4 - Prob. 5ECh. 1.4 - Prob. 6ECh. 1.4 - In Exercises 6–8, determine whether the statement...Ch. 1.4 - Prob. 8ECh. 1.4 - In Exercises 9–16, specify the type of bias...Ch. 1.4 - In Exercises 9–16, specify the type of bias...Ch. 1.4 - In Exercises 9–16, specify the type of bias...Ch. 1.4 - In Exercises 9–16, specify the type of bias...Ch. 1.4 - In Exercises 9–16, specify the type of bias...Ch. 1.4 - In Exercises 9–16, specify the type of bias...Ch. 1.4 - Prob. 15ECh. 1.4 - In Exercises 9–16, specify the type of bias...Ch. 1.4 - Nuclear power, anyone? In a survey conducted by...Ch. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Literary Digest poll: In the 1936 presidential...Ch. 1 - Provide an example of a qualitative variable and...Ch. 1 - Is the name of your favorite author a qualitative...Ch. 1 - True or false: Nominal variables do not have a...Ch. 1 - Prob. 4CQCh. 1 - Prob. 5CQCh. 1 - Prob. 6CQCh. 1 - Prob. 7CQCh. 1 - Prob. 8CQCh. 1 - True or false: An experiment where neither the...Ch. 1 - Prob. 10CQCh. 1 - Prob. 11CQCh. 1 - Prob. 12CQCh. 1 - Prob. 13CQCh. 1 - Prob. 14CQCh. 1 - Prob. 15CQCh. 1 - Prob. 1RECh. 1 - Prob. 2RECh. 1 - Discrete or continuous? Is the area of a college...Ch. 1 - Prob. 4RECh. 1 - In Exercises 5–8, identify the kind of sample that...Ch. 1 - In Exercises 5–8, identify the kind of sample that...Ch. 1 - Prob. 7RECh. 1 - In Exercises 5–8, identify the kind of sample that...Ch. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - In Exercises 13–15, explain why the results of the...Ch. 1 - In Exercises 13–15, explain why the results of the...Ch. 1 - In Exercises 13–15, explain why the results of the...Ch. 1 - Prob. 1WAICh. 1 - Prob. 2WAICh. 1 - Describe circumstances under which each of the...Ch. 1 - Prob. 4WAICh. 1 - Prob. 5WAICh. 1 - Prob. 6WAICh. 1 - Prob. 7WAICh. 1 - Prob. 9WAICh. 1 - Prob. 1CSCh. 1 - Prob. 2CSCh. 1 - Prob. 3CSCh. 1 - Prob. 4CSCh. 1 - Prob. 5CSCh. 1 - Prob. 6CSCh. 1 - Prob. 7CSCh. 1 - Prob. 8CSCh. 1 - Prob. 9CSCh. 1 - Prob. 10CSCh. 1 - Prob. 11CSCh. 1 - Air pollution is a serious problem in many places....
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