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IS 310 – Business Statistics
Business
Statistics
IS 310
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CSU
LONG
BEACH

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IS 310 – Business Statistics
Chapter 12
Comparing Multiple Proportions,
Test of Independence and Goodness of Fit
Testing the Equality of Population Proportions
for Three or More Populations
Goodness of Fit Test
Test of Independence

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IS 310 – Business Statistics
Comparing Multiple Proportions,
Test of Independence and Goodness of Fit
In this chapter we introduce three additional
hypothesis-testing procedures.
The test statistic and the distribution used are
based on the chi-square (
2
) distribution.
In all cases, the data are categorical.

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IS 310 – Business Statistics
Using the notation
p
1
= population proportion for
population 1
p
2
= population proportion for
population 2
and
p
k
= population proportion for
population
k
H
0
:
p
1
=
p
2
=
.
.
.
=
p
k
H
a
:
Not all population proportions are
equal
Testing the Equality of Population
Proportions
for Three or More Populations
The hypotheses for the equality of population
proportions for
k
>
3 populations are as
follows:

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IS 310 – Business Statistics
If
H
0
cannot be rejected, we cannot detect a
difference among the
k
population
proportions.
If
H
0
can be rejected, we can conclude that
not all
k
population proportions are equal.
Further analyses can be done to conclude
which population proportions are significantly
different from others.
Testing the Equality of Population
Proportions
for Three or More Populations

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IS 310 – Business Statistics
Example:
Finger Lakes Homes
Finger Lakes Homes manufactures three
models of
prefabricated homes, a two-story colonial, a log
cabin,
and an A-frame.
To help in product-line
planning,
management would like to compare the
customer
satisfaction with the three home styles.
Testing the Equality of Population
Proportions
for Three or More Populations
p
1
= proportion likely to repurchase a
Colonial
for the population of Colonial owners
p
2
= proportion likely to repurchase a Log
Cabin
for the population of Log Cabin
owners
p
3
= proportion likely to repurchase an A-

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IS 310 – Business Statistics
We begin by taking a sample of owners from
each of the three populations.
Each sample contains categorical data indicating
whether the respondents are likely or not likely
to
repurchase the home.
Testing the Equality of Population
Proportions
for Three or More Populations

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IS 310 – Business Statistics
Home Owner
Colonial
Log
A-Frame
Total
Likely to
Yes
100
81
83
264
Repurchase
No
35
20
41
96
Total
135
101
124
360
Observed Frequencies (sample results)
Testing the Equality of Population
Proportions
for Three or More Populations

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IS 310 – Business Statistics
Next, we determine the expected frequencies
under the assumption
H
0
is correct.

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