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Maumee Ford-Mercury: Relationship Between Care Age And Selling Price

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.

Car Age (years) Selling Price ($000) Car Age (years) Selling Price ($000)
1 9 8.1 7 8 7.6
2 7 6.0 8 11 8.0
3 11 3.6 9 10 8.0
4 12 4.0 10 12 6.0
5 8 5.0 11 6 8.6
6 7 10.0 12 6 8.0

Determine the coefficient of correlation.
Determine the coefficient of determination.

Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship
between the number of client contacts and the dollar amount of sales. To document
this assertion, Mr. McWhinney gathered the following sample information. The X
column indicates the number of client contacts last month, and the Y column shows the
value of sales ($ thousands) last month for each client sampled.

Number of Sales Number of Sales
Contacts, ($ thousands), Contacts, ($ thousands),
X Y X Y
14 24 23 30
12 14 48 90
20 28 50 85
16 30 55 120
46 80 50 110

a. Determine the regression equation.
b. Determine the estimated sales if 40 contacts are made.

The following sample observations were randomly selected.

X: 5 3 6 3 4 4 6 8
Y: 13 15 7 12 13 11 9 5
a. Determine the standard error of estimate.
b. Suppose a large sample is selected (instead of just eight). About 95 percent of the predictions
would be between what two values?

Number of Sales Number of Sales
Contacts, ($ thousands), Contacts, ($ thousands),
X Y X Y
14 24 23 30
12 14 48 90
20 28 50 85
16 30 55 120
46 80 50 110

a. Determine the .95 confidence interval, in thousands of dollars, for the mean of all sales
personnel who make 40 contacts.
b. Determine the .95 prediction interval, in thousands of dollars, for a particular salesperson
who makes 40 contacts.

The Tampa Bay (Florida) Area Chamber of Commerce wanted to know whether the mean
weekly salary of nurses was larger than that of school teachers. To investigate, they collected
the following information on the amounts earned last week by a sample of school
teachers and nurses.

School teachers ($) 845 826 827 875 784 809 802 820 829 830 842 832
Nurses ($) 841 890 821 771 850 859 825 829

Is it reasonable to conclude that the mean weekly salary of nurses is higher? Use the .01
significance level. What is the p-value?

The federal government recently granted funds for a special program designed to reduce
crime in high-crime areas. A study of the results of the program in eight high-crime areas of
Miami, Florida, yielded the following results.

A Number of Crimes by Area
B C D E F G H
Before 14 7 4 5 17 12 8 9
After 2 7 3 6 8 13 3 5

Has there been a decrease in the number of crimes since the inauguration of the program?
Use the .01 significance level. Estimate the p-value.

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Detailed explanation of case study, with all relevant calculations and tests.

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