Mathematical Statistics with Applications
7th Edition
ISBN: 9781111798789
Author: Dennis O. Wackerly
Publisher: Cengage Learning
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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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The table below shows the prices (R) and quantities (kg) of rice, meat and potatoes items bought during 2013 and 2014:
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Q Search
ENG US
口X
2025/05
The table below indicates the number of years of experience of a sample of employees who work on a particular production line and the corresponding number of units of a good that each employee produced last month.
Years of Experience (x)
Number of Goods (y)
11
63
5
57
1
48
4
54
45
3
51
Q.1.1 By completing the table below and then applying the relevant formulae, determine the line of best fit for this bivariate data set.
Do NOT change the units for the variables.
X
y
X2
xy
Ex=
Ey=
EX2
EXY=
Q.1.2 Estimate the number of units of the good that would have been produced last month by an employee with 8 years of experience.
Q.1.3 Using your calculator, determine the coefficient of correlation for the data set.
Interpret your answer.
Q.1.4 Compute the coefficient of determination for the data set.
Interpret your answer.
Q.3.2 A sample of consumers was asked to name their favourite fruit. The results regarding the popularity of the different fruits are given in the following table.
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Chapter 7 Solutions
Mathematical Statistics with Applications
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