Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Question
Chapter 9.3, Problem 11E
a.
To determine
Find all the main and interaction effects.
b.
To determine
Construct an ANOVA table and the find the
c.
To determine
Explain whether the additive model is plausible.
d.
To determine
Check whether the effects of material on coefficient of friction can be described by the main effects of material.
e.
To determine
Check whether the effects of neck length on coefficient of friction can be described by the main effects of neck length. If so, interpret the main effects by multiple comparisons at the 5% level. If not explain the reason.
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Artificial joints consist of a ceramic ball mounted on a taper. The article "Friction in
Orthopaedic Zirconia Taper Assemblies" (W. Macdonald, A. Áspenberg, et al., Proceedings
of the Institution of Mechanical Engineers, 2000: 685-692) presents data on the coefficient
of friction for a push-on load of 2 kN for taper assemblies made from two zirconium alloys
and employing three different neck lengths. Five measurements were made for each
combination of material and neck length. The results presented in the following table are
consistent with the cell means and standard deviations presented in the article.
Тарег
Material
Neck
Length
Coefficient of Friction
CPTI-ZIO2
CPTI-Z:O,
CPTI-Z:O, Long
TIAlloy-ZrO, Short
TiAlloy-ZrO, Medium
TiAlloy-ZrO, Long
Short
0.254 0.195 0.281 0.289 0.220
Medium
0.196 0.220 0.185 0.259 0.197
0.329 0.481 0.320 0.296 0.178
0.150 0.118 0.158 0.175 0.131
0.180 0.184 0.154 0.156 0.177
0.178 0.198 0.201 0.199 0.210
Compute the main effects and interactions.
Construct…
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.
Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below.
I
II
III
5.5
5.2
6.8
4.6
6.5
5.3
5.1
6.1
4.4
5.5
4.1
7.9
4.1
5.1
5.9
5.4
6.1
6.9
5.4
5.1
6.6
Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 5% level of significance.
(a) What is the level of significance?State the null and alternate hypotheses.
Ho: ?1 = ?2 = ?3; H1: Exactly two means are equal.Ho: ?1 = ?2 = ?3; H1: Not all the means are equal. Ho: ?1 = ?2 = ?3; H1:…
Chapter 9 Solutions
Statistics for Engineers and Scientists
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- Wild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below. I II III 5.7 5.4 6.8 4.1 6.3 5.4 5.0 6.7 4.4 5.4 4.3 7.3 4.6 5.5 5.3 5.7 6.5 6.7 5.2 5.3 6.8 Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 5% level of significance. (a) What is the level of significance?State the null and alternate hypotheses. Ho: ?1 = ?2 = ?3; H1: All three means are different.Ho: ?1 = ?2 = ?3; H1: Not all the means are equal. Ho: ?1 = ?2 = ?3;…arrow_forwardWild irises are beautiful flowers found throughout the United States, Canada, and northern Europe. This problem concerns the length of the sepal (leaf-like part covering the flower) of different species of wild iris. Data are based on information taken from an article by R. A. Fisher in Annals of Eugenics (Vol. 7, part 2, pp. 179 -188). Measurements of sepal length in centimeters from random samples of Iris setosa (I), Iris versicolor (II), and Iris virginica (III) are as follows below. I II III 5.9 5.8 6.9 4.8 6.5 5.6 4.6 6.4 4.9 5.7 4.3 7.7 4.8 5.8 5.6 5.4 6.3 6.3 5.8 5.5 6.6 Shall we reject or not reject the claim that there are no differences among the population means of sepal length for the different species of iris? Use a 5% level of significance. (b) Find SSTOT, SSBET, and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.) SSTOT = SSBET = SSW = Find d.f.BET, d.f.W, MSBET, and MSW. (Use 4 decimal places for MSBET, and…arrow_forwardThe article " The Ball-on-Three-Ball Test for Tensile Strength: Refined Methodology and Results for Three Hohokam Ceramic Types" (M. Beck, American Antiquity, 2002:558-569) discusses the strength of ancient ceramics. Several specimens of each of three types of ceramic were tested. The loads (in kg) required to caack the specimens are as follows: Ceramic Loads (kg) Type Sacaton 15, 30, 51, 20, 17, 19, 20, 32, 17, 15, 23, 19, 15, 18, 16, 22, 29, 15, 13, 15 27, 18, 28, 25, 55, 21, 18, 34, 23, 30, 20, 30, 31, 25, 28, 26, 17, 19, 16, 24, 19, 9, 31, 19, 27, 20, 43, 15 20, 16, 20, 36, 27, 35, 66, 15, 18, 24, 21, 30, 20, 24, Gila Plain Casa Grande 23, 21, 13, 21 Construct comparative boxplots for the three samples. b. How many outliers does each sample contain? c Comment on the features of the three samples.arrow_forward
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