Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Textbook Question
Chapter 1, Problem 73SE
The article “Can We Really Walk Straight?” (Amer. J. of Physical Anthropology, 1992: 19-27) reported on an experiment in which each of 20 healthy men was asked to walk as straight as possible to a target 60 m away at normal speed. Consider the following observations on cadence (number of strides per second):
Use the methods developed in this chapter to summarize the data; include an interpretation or discussion wherever appropriate. [Note: The author of the article used a rather sophisticated statistical analysis to conclude that people cannot walk in a straight line and suggested several explanations for this.]
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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
Probability and Statistics for Engineering and the Sciences
Ch. 1.1 - Give one possible sample of size 4 from each of...Ch. 1.1 - For each of the following hypothetical...Ch. 1.1 - Consider the population consisting of all...Ch. 1.1 - a. Give three different examples of concrete...Ch. 1.1 - Many universities and colleges have instituted...Ch. 1.1 - The California State University (CSU) system...Ch. 1.1 - A certain city divides naturally into ten district...Ch. 1.1 - The amount of flow through a solenoid valve in an...Ch. 1.1 - In a famous experiment carried out in 1882,...Ch. 1.2 - Consider the strength data for beams given in...
Ch. 1.2 - The accompanying specific gravity values for...Ch. 1.2 - The accompanying summary data on CeO2 particle...Ch. 1.2 - Allowable mechanical properties for structural...Ch. 1.2 - The accompanying data set consists of observations...Ch. 1.2 - Do running limes of American movies differ somehow...Ch. 1.2 - The article cited in Example 1.2 also gave the...Ch. 1.2 - The accompanying data came from a study of...Ch. 1.2 - Every corporation has a governing board of...Ch. 1.2 - The number of contaminating particles on a silicon...Ch. 1.2 - The article Determination of Most Representative...Ch. 1.2 - The article cited in Exercise 20 also gave the...Ch. 1.2 - How does the speed of a runner vary over the...Ch. 1.2 - The article Statistical Modeling of the Time...Ch. 1.2 - The accompanying data set consists of observations...Ch. 1.2 - A transformation of data values by means of some...Ch. 1.2 - The accompanying summary data on CeO2 particle...Ch. 1.2 - The article Study on the Life Distribution of...Ch. 1.2 - The accompanying frequency distribution on...Ch. 1.2 - The following categories for type of physical...Ch. 1.2 - A Pareto diagram is a variation of a histogram for...Ch. 1.2 - The cumulative frequency and cumulative relative...Ch. 1.2 - Fire load (MJ/m2) is the heat energy that could be...Ch. 1.3 - The May 1, 2009, issue of The Montclarian reported...Ch. 1.3 - Exposure to microbial products, especially...Ch. 1.3 - Mercury is a persistent and dispersive...Ch. 1.3 - A sample of 26 offshore oil workers took part in a...Ch. 1.3 - The article Snow Cover and Temperature...Ch. 1.3 - Blood pressure values are often reported to the...Ch. 1.3 - The propagation of fatigue cracks in various...Ch. 1.3 - Compute the sample median. 25% trimmed mean. 10%...Ch. 1.3 - A sample of n = 10 automobiles was selected, and...Ch. 1.3 - a. If a constant c is added to each xi in a...Ch. 1.3 - An experiment to study the lifetime (in hours) for...Ch. 1.4 - Poly(3-hydroxybutyrate) (PHB), a semicrystalline...Ch. 1.4 - The value of Youngs modulus (GPa) was determined...Ch. 1.4 - The article Effects of Short-Term Warming on Low...Ch. 1.4 - Zinfandel is a popular red wine varietal produced...Ch. 1.4 - Exercise 34 presented the following data on...Ch. 1.4 - A study of the relationship between age and...Ch. 1.4 - In 1997 a woman sued a computer keyboard...Ch. 1.4 - The article A Thin-Film Oxygen Uptake Test for the...Ch. 1.4 - The first four deviations from the mean in a...Ch. 1.4 - A mutual fund is a professionally managed...Ch. 1.4 - Grip is applied to produce normal surface forces...Ch. 1.4 - Here is a stem-and-leaf display of the escape time...Ch. 1.4 - The following data on distilled alcohol content...Ch. 1.4 - A sample of 20 glass bottles of a particular type...Ch. 1.4 - A company utilizes two different machines to...Ch. 1.4 - Blood cocaine concentration (mg/L) was determined...Ch. 1.4 - Observations on burst strength (lb/in2) were...Ch. 1.4 - The accompanying comparative boxplot of gasoline...Ch. 1 - Consider the following information on ultimate...Ch. 1 - A sample of 77 individuals working at a particular...Ch. 1 - Fretting is a wear process that results from...Ch. 1 - The accompanying frequency distribution of...Ch. 1 - A deficiency of the (race element selenium in the...Ch. 1 - Aortic stenosis refers to a narrowing of the...Ch. 1 - a. For what value of c is the quantity (xi c)2...Ch. 1 - a. Let a and b be constants and let yi = axi + b...Ch. 1 - Elevated energy consumption during exercise...Ch. 1 - Here is a description from Minitab of the strength...Ch. 1 - Anxiety disorders and symptoms can often be...Ch. 1 - The article Can We Really Walk Straight? (Amer. J....Ch. 1 - The mode of a numerical data set is the value that...Ch. 1 - Specimens of three different types of rope wire...Ch. 1 - The three measures of center introduced in this...Ch. 1 - The authors of the article Predictive Model for...Ch. 1 - Consider a sample x1 , x2,..., xn and suppose that...Ch. 1 - Let xn and sn2 denote the sample mean and variance...Ch. 1 - Lengths of bus routes for any particular transit...Ch. 1 - A study carried out to investigate the...Ch. 1 - Prob. 82SECh. 1 - Prob. 83SECh. 1 - Consider a sample x1, ... , xn with n even. Let xL...
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