Mathematical Statistics with Applications
7th Edition
ISBN: 9781133384380
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
Publisher: Cengage Learning US
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Chapter 7.2, Problem 28E
Applet Exercise Suppose that Y has an F distribution with ν1 = 4 numerator degrees of freedom and ν2 = 6 denominator degrees of freedom.
- a Use Table 7, Appendix 3, to find F.025. Also find F.025 using the applet F-Ratio
Probabilities and Quantiles. - b Refer to part (a). What quantile of Y does F.025 correspond to? What percentile?
- c Refer to parts (a) and (b). Use the applet F-Ratio Probabilities and Quantiles to find F.975, the .025 quantile (2.5th percentile) of the distribution of Y.
- d If U has an F distribution with ν1 = 6 numerator and ν2 = 4 denominator degrees of freedom, use Table 7, Appendix 3, or the F-Ratio Probabilities and Quantiles applet to find F.025.
- e In Exercise 7.29, you will show that if Y is a random variable that has an F distribution with ν1 numerator and ν2 denominator degrees of freedom, then U = 1/Y has an F distribution with ν2 numerator and ν1 denominator degrees of freedom. Does this result explain the relationship between F.975 from part (c) (4 numerator and 6 denominator degrees of freedom) and F.025 from part (d) (6 numerator and 4 denominator degrees of freedom)? What is this relationship?
7.29 If Y is a random variable that has an F distribution with ν1 numerator and ν2 denominator degrees of freedom, show that U = 1/Y has an F distribution with ν2 numerator and ν1 denominator degrees of freedom.
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Question 4
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A222222222222233
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Table 3: Silver Powder Experiment from Exercise 13.23
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++
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
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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).
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C = +?
(d) Repeat…
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data are shown in Table 2.
1
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(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).
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Chapter 7 Solutions
Mathematical Statistics with Applications
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