Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
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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ons
12. A sociologist hypothesizes that the crime rate is higher in areas
with higher poverty rate and lower median income. She col-
lects data on the crime rate (crimes per 100,000 residents),
the poverty rate (in %), and the median income (in $1,000s)
from 41 New England cities. A portion of the regression results
is shown in the following table.
Standard
Coefficients
error
t stat
p-value
Intercept
-301.62
549.71
-0.55 0.5864
Poverty
53.16
14.22
3.74 0.0006
Income
4.95
8.26
0.60 0.5526
a.
b.
Are the signs as expected on the slope coefficients?
Predict the crime rate in an area with a poverty rate of
20% and a median income of $50,000.
3. Using data from 50 work
2. The owner of several used-car dealerships believes that the
selling price of a used car can best be predicted using the car's
age. He uses data on the recent selling price (in $) and age of
20 used sedans to estimate Price = Po + B₁Age + ε. A portion
of the regression results is shown in the accompanying table.
Standard
Coefficients
Intercept
21187.94
Error
733.42
t Stat p-value
28.89 1.56E-16
Age
-1208.25
128.95 -9.37
2.41E-08
a. What is the estimate for B₁? Interpret this value.
b. What is the sample regression equation?
C. Predict the selling price of a 5-year-old sedan.
ian income of $50,000.
erty rate of
13. Using data from 50 workers, a researcher estimates Wage =
Bo+B,Education + B₂Experience + B3Age+e, where Wage
is the hourly wage rate and Education, Experience, and Age
are the years of higher education, the years of experience, and
the age of the worker, respectively. A portion of the regression
results is shown in the following table. ni ogolloo bash
1
Standard
Coefficients error
t stat p-value
Intercept
7.87
4.09
1.93
0.0603
Education
1.44
0.34
4.24 0.0001
Experience
0.45
0.14
3.16
0.0028
Age
-0.01
0.08 -0.14 0.8920
a. Interpret the estimated coefficients for Education and
Experience.
b. Predict the hourly wage rate for a 30-year-old worker
with four years of higher education and three years of
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Chapter 7 Solutions
Mathematical Statistics with Applications
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