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STA2023 – Chapter 22 (Comparing Two Proportions)
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Pooling (pages 565566)
In chapters 19 & 20, you learned how to create confidence intervals and run hypothesis tests for a single
population proportion (
p
).
This chapter explains how to create confidence intervals and run hypothesis
tests for comparing the proportion of successes between two populations (comparing
p
1
versus
p
2
).
In
other words, we will be making
inferences about how two groups differ
.
In the real world of statistics,
comparing two populations is far more common than drawing an inference about a single population.
A nutritionist wishes to do a study to see if there is a difference in the percentage of females living in
Florida versus males living in Florida who consume too much saturated fat.
Based on interviews with
400 randomly selected Florida males, she determines that 278 consume too much saturated fat.
Based on
interviews with 400 randomly selected Florida females, she determines that 234 consume too much
saturated fat.
A. This study is comparing two different populations.
Describe them (be specific)
Population 1:
Population 2:
B. Are the populations independent or dependent?
Explain your choice.
C. If we define a success as someone who consumes too much saturated fat, what is the proportion of
successes in each sample?
^
1
p
=
^
males
p
=
^
2
p
=
^
females
p
=
Note that n
1
= n
2
= 400.
Often times, when comparing two populations, the samples are the same
size.
However, since the populations are independent of each other, it is not necessary that n
1
= n
2
D. Note that this study is comparing the proportion of successes from two independent populations.
The
difference in the proportion of successes between the samples is:
^
^
^
^
1
2
males
females
p
p
p
p

=

= 0.11
Explain what this value means in the context of the given scenario.
Because of sampling variability, this difference of 11% is only a point estimate.
If another sample
of males and females was taken, the difference between the proportions of those males versus
females that consume too much saturated fat could be something other than 11%.
As such, we
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 Spring '08
 Ripol
 Statistics

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