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# Solution to some stats problems

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CHAP. 12

18. There are three hospitals in the Tulsa, Oklahoma, area. The following data show the number
of outpatient surgeries performed at each hospital last week. At the .05 significance level,
can we conclude there is a difference in the mean number of surgeries performed by hospital
or by day of the week?

CHAP 13

6. The owner of Maumee Ford-Mercury wants to study the relationship between the age of a
car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership
during the last year.

a. If we want to estimate selling price on the basis of the age of the car, which variable is
the dependent variable and which is the independent variable?
b. Draw a scatter diagram.
c. Determine the coefficient of correlation.
d. Determine the coefficient of determination.
e. Interpret these statistical measures. Does it surprise you that the relationship is inverse?

16. We are studying mutual bond funds for the purpose of investing in several funds. For this
particular study, we want to focus on the assets of a fund and its five-year performance.
The question is: Can the five-year rate of return be estimated based on the assets of the
fund? Nine mutual funds were selected at random, and their assets and rates of return are
shown below.

a. Draw a scatter diagram.
b. Compute the coefficient of correlation.
c. Compute the coefficient of determination.
d. Write a brief report of your findings for parts b and c.
e. Determine the regression equation. Use assets as the independent variable.
f. For a fund with \$400.0 million in sales, determine the five-year rate of return (in percent).

CHAP 14.

16. The following problems require a software package.

Mike Wilde is president of the teachers' union for Otsego School District. In preparing for upcoming
negotiations, he would like to investigate the salary structure of classroom teachers
in the district. He believes there are three factors that affect a teacher's salary: years of experience,
a rating of teaching effectiveness given by the principal, and whether the teacher
has a master's degree. A random sample of 20 teachers resulted in the following data.

a. Develop a correlation matrix. Which independent variable has the strongest correlation
with the dependent variable? Does it appear there will be any problems with multicollinearity?
b. Determine the regression equation. What salary would you estimate for a teacher with
five years' experience, a rating by the principal of 60, and no master's degree?
c. Conduct a global test of hypothesis to determine whether any of the net regression coefficients
differ from zero. Use the .05 significance level.
d. Conduct a test of hypothesis for the individual regression coefficients. Would you consider
deleting any of the independent variables? Use the .05 significance level.
e. If your conclusion in part (d) was to delete one or more independent variables, run the
analysis again without those variables.
f. Determine the residuals for the equation of part (e). Use a stem-and-leaf chart or a histogram
to verify that the distribution of the residuals is approximately normal.
g. Plot the residuals computed in part (f) in a scatter diagram with the residuals on the Yaxis
and the Y_ values on the X-axis. Does the plot reveal any violations of the assumptions
of regression?
0.70
0.35
0.00
-0.35
1.50 2.00 2.50 3.00 3.50 4.00
Residuals (Y - Y')
Y
22. A mortgage department of a large bank is studying its recent loans. Of particular interest is how such factors as the value of the home (in thousands of dollars), education level of the head of the household, age of the head of the household, current monthly mortgage payment (in dollars), and gender of the head of the household (male _ 1, female _ 0) relate to the family income. Are these variables effective predictors of the income of the household?
A random sample of 25 recent loans is obtained.

a.Determine the regression equation.
b. What is the value of R2? Comment on the value.
c. Conduct a global hypothesis test to determine whether any of the independent variables
are different from zero.
d. Conduct individual hypothesis tests to determine whether any of the independent variables
can be dropped.
e. If variables are dropped, recompute the regression equation and R2.

CHAP 15

26. A study regarding the relationship between age and the amount of pressure sales personnel
feel in relation to their jobs revealed the following sample information. At the .01 significance
level, is there a relationship between job pressure and age?
Nonparametric Methods: Chi-Square Applications 541

CHAP 16

26. Far West University offers both day and evening classes in business administration. One
question in a survey of students inquires how they perceive the prestige associated with
certain careers. Each student was asked to rank the careers from 1 to 8, with 1 having the
most prestige and 8 the least prestige. The results were:

Find Spearman's coefficient of rank correlation.

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