PMBA 305 Module #4: Two-Sample Tests and Simple Linear Regression Spring ’13

PMBA 305 – Spring ’13
Quantitative Aspects of Decision Making
Module #4: Two-Sample
Tests and Simple Linear Regression
[1]
In an article in Marketing Science,
Silk and Berndt investigate the output of advertising agencies. They describe ad agency output by finding the
shares of dollar billing volume coming from various media categories such as
network television, spot television, newspaper, radio, and so forth.
Suppose
that a random sample of 400 U.S. advertising agencies gives an average
percentage share of billing volume from network television equal to 7.46
percent with a standard deviation of 1.42 percent. Further, suppose that a random sample of 400
U.S. advertising agencies gives an average percentage share of billing volume
from spot television commercials equal to 12.44 percent with a standard
deviation of 1.55 percent.
Using
the sample information, does it appear that the mean percentage share of
billing volume from spot television commercials for the U.S. advertising
agencies is greater than the mean percentage share of billing volume from
network television? Explain.

[2] A random sample of the birth weights of 186 babies has a mean
of 3103g and a standard deviation of 696g (based on data from “Cognitive
Outcomes of Preschool Children with Prenatal Cocaine Exposure,” by Singer et
al., Journal of the American Medical
Association, Vol. 291, No. 20).
These babies were born to mothers who did not use cocaine during their
pregnancies. Further, a random sample of
the birth weights of 190 babies born to mothers who used cocaine during their pregnancies
has a mean of 2700g and a standard deviation of 645g. Does cocaine use appear to affect the birth
weight of a baby? Substantiate you
conclusion.

[4]
An auto manufacturing company wanted to investigate how the price of one of its
car models depreciates with age. The
research department at the company took a sample of eight cars of this model
and collected the following information on the ages (in years) and prices (in
hundreds of dollars) of these cars. The
data are in USEDCAR.xls.

Age (x)

8

3

6

9

2

5

6

3

Price (y)

16

74

40

19

124

36

33

89

a)
Find
the value of the linear correlation coefficient r.
b)
Find
the value of the coefficient of determination r2, and interpret the
meaning for this problem.
c)
At
the 0.05 level of significance, is there a significant linear relationship
between two variables?
d)
Determine
the adequacy of the fit of the model.
e)
Evaluate
whether the assumptions of regression (LINE) have been seriously violated.
f)
If
there is a linear correlation, what is the regression equation?
g)
Interpret
the meaning of the slope b1 in this problem.
h)
Interpret
the meaning of the Y-intercept b0 in this problem. Will it make sense to you as far as this
model is concerned? Explain why.
i)
Set
up a 95% confidence interval estimate of the population slope.
j)
Set
up a 95% confidence interval estimate of the average price for all cars of this
model after 7 years.
k)
Set
up a 95% confidence interval of the average price of a car of this model after
7 years.
l)
Explain
the difference in the results obtained in (j) and (k).