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 4.6, Problem 92E
The article “The Load-Life Relationship for M50 Bearings with Silicon Nitride Ceramic Balls” (Lubrication Engr., 1984: 153–159) reports the accompanying data on bearing load life (million revs.) for bearings tested at a 6.45 kN load.
47.1 | 68.1 | 68.1 | 90.8 | 103.6 | 106.0 | 115.0 |
126.0 | 146.6 | 229.0 | 240.0 | 240.0 | 278.0 | 278.0 |
289.0 | 289.0 | 367.0 | 385.9 | 392.0 | 505.0 |
a. Construct a normal probability plot. Is normality plausible?
b. Construct a Weibull probability plot. Is the Weibull distribution family plausible? Copyright
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following table.
X1
X2
y
32
20.0
28
39
23.0
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12.8
32
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a. Fit the model y = Bo + B1 X1 + ɛ. For each coefficient, test the null hypothesis that it is
equal to 0.
b. Fit the model y = Bo + B, xz + ɛ. For each coefficient, test the null hypothesis that it is
equal to 0.
c. Fit the model y = Bo + B1 X1 + Bzx2 + ɛ. For each coefficient, test the null hypothesis
that it is equal to 0.
d. Which of the models in parts (a) through (c) is the best of the three? Why do you think
%3D
+ E.
so?
The following are the weight losses of certain machine parts due to friction (in milligrams) when used with three different lubricants:
Lubricant 1:
13
11
10
13
Lubricant 2:
9.
11
Lubricant 3:
7
6.
Test at the 0,01 level of significance whether the type of lubricant effects the weight loss of the machine parts due to friction. While
carrying out the test, follow the steps below and answer the questions.
1- Determine the null and alternative hypotheses.
Ho:
H:
2-Fill in the following ANOVA Table.
ANOVA Table
Source of Variation Degrees of Freedom
Sum of Squares Mean Sum of Squares
Treatment
Error
Total
3-State your decision and conclusion.
An experiment was conducted to study the extrusion process of biodegradable packaging foam. Two of the factors considered for their effect on
the unit density (mg/ml) were the die temperature (145 °C vs. 155 °C) and the die diameter (3 mm vs. 4 mm). The results are stored in [Packaging
Foam 1]. Source: Data extracted from W. Y. Koh, K. M. Eskridge, and M. A. Hanna, "Supersaturated Split-Plot Designs," Journal of Quality
Technology, 45, January 2013, pp. 61-72.At the 0.05 level of significance,
3mm 4mm
57.22
145
72.54
145 53.60 66.70
145 48.13
49.28
145 69.89 44.14
145 62.78
58.37
145 55.18
53.98
155 57.50
63.03
155 54.17 46.73
155 73.86 60.17
155 90.28 46.78
155 88.19 43.27
155 82.61 56.93
Die Temperature
a. is there an interaction between die temperature and die diameter?
b. is there an effect due to die temperature?
c. is there an effect due to die diameter?
d. Plot the mean unit density for each die temperature for each die diameter.
e. What can you conclude about the effect of die…
Chapter 4 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 4.1 - The current in a certain circuit as measured by an...Ch. 4.1 - Suppose the reaction temperature X (in C) in a...Ch. 4.1 - The error involved in making a certain measurement...Ch. 4.1 - Let X denote the vibratory stress (psi) on a wind...Ch. 4.1 - A college professor never finishes his lecture...Ch. 4.1 - The actual tracking weight of a stereo cartridge...Ch. 4.1 - The article Second Moment Reliability Evaluation...Ch. 4.1 - Prob. 8ECh. 4.1 - Based on an analysis of sample data, the article...Ch. 4.1 - A family of pdfs that has been used to approximate...
Ch. 4.2 - Let X denote the amount of time a book on two-hour...Ch. 4.2 - The cdf for X (= measurement error) of Exercise 3...Ch. 4.2 - Prob. 13ECh. 4.2 - The article Modeling Sediment and Water Column...Ch. 4.2 - Let X denote the amount of space occupied by an...Ch. 4.2 - The article A Model of Pedestrians Waiting Times...Ch. 4.2 - Let X have a uniform distribution on the interval...Ch. 4.2 - Let X denote the voltage at the output of a...Ch. 4.2 - Let X be a continuous rv with cdf...Ch. 4.2 - Consider the pdf for total waiting time Y for two...Ch. 4.2 - An ecologist wishes to mark off a circular...Ch. 4.2 - The weekly demand for propane gas (in 1000s of...Ch. 4.2 - If the temperature at which a certain compound...Ch. 4.2 - Let X have the Pareto pdf f(x;k,)={kkxk+1x0x...Ch. 4.2 - Let X be the temperature in C at which a certain...Ch. 4.2 - Let X be the total medical expenses (in 1000s of...Ch. 4.2 - Prob. 27ECh. 4.3 - Let Z be a standard normal random variable and...Ch. 4.3 - In each case, determine the value of the constant...Ch. 4.3 - Find the following percentiles for the standard...Ch. 4.3 - Determine z for the following values of : a. =...Ch. 4.3 - Suppose the force acting on a column that helps to...Ch. 4.3 - Mopeds (small motorcycles with an engine capacity...Ch. 4.3 - The article Reliability of Domestic-Waste Biofilm...Ch. 4.3 - In a road-paving process, asphalt mix is delivered...Ch. 4.3 - Spray drift is a constant concern for pesticide...Ch. 4.3 - Suppose that blood chloride concentration (mmol/L)...Ch. 4.3 - There are two machines available for cutting corks...Ch. 4.3 - The defect length of a corrosion defect in a...Ch. 4.3 - The article Monte Carlo SimulationTool for Better...Ch. 4.3 - The automatic opening device of a military cargo...Ch. 4.3 - The temperature reading from a thermocouple placed...Ch. 4.3 - Vehicle speed on a particular bridge in China can...Ch. 4.3 - If bolt thread length is normally distributed,...Ch. 4.3 - A machine that produces ball bearings has...Ch. 4.3 - The Rockwell hardness of a metal is determined by...Ch. 4.3 - The weight distribution of parcels sent in a...Ch. 4.3 - Suppose Appendix Table A.3 contained (z) only for...Ch. 4.3 - Consider babies born in the normal range of 3743...Ch. 4.3 - In response to concerns about nutritional contents...Ch. 4.3 - Chebyshevs inequality, (see Exercise 44, Chapter...Ch. 4.3 - Let X denote the number of flaws along a 100-m...Ch. 4.3 - Let X have a binomial distribution with parameters...Ch. 4.3 - Suppose that 10% of all steel shafts produced by a...Ch. 4.3 - Suppose only 75% of all drivers in a certain state...Ch. 4.3 - Show that the relationship between a general...Ch. 4.3 - a. 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