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Rev. F08
http://faculty.valenciacc.edu/ashaw/
1
STA 2023
Module 12
Inferences for Population
Proportions
Rev.F08
2
Learning Objectives
Upon completing this module, you should be able to:
1.
Find a largesample confidence interval for a population
proportion.
2.
Compute the margin of error for the estimate of a population
proportion.
3.
Understand the relationship between the sample size,
confidence interval, and margin of error for a confidence
interval for a population proportion.
4.
Determine the sample size required for a specified confidence
level and margin of error for the estimate of a population
proportion.
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valenciacc
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Rev.F08
3
Learning Objectives
5.
Perform a largesample hypothesis test for a population
proportion.
6.
Perform largesample inferences (hypothesis test and
confidence intervals) to compare two population proportions.
7.
Understand the relationship between the sample sizes,
confidence level, and margin of error for a confidence interval
for the difference between two population proportions.
8.
Determine the sample size required for a specified confidence
level and margin of error for the estimate of the difference
between two population proportions.
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Rev.F08
4
What is Population Proportion?
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In the last three modules, we examined various methods for
finding confidence intervals and performing hypothesis tests
for
one or two population means
.
In this module, we are going to learn
how to perform those
inferences for one or two populations proportions
.
What is population proportion?
A
population proportion,
p,
is simply the percentage of a
population that has a specified attribute.
Rev.F08
5
Population Proportion
and Sample Proportion
In short, a
sample proportion
is obtained by dividing
the number of members sampled
that have the specified attribute (x)
by the
total number of members sampled (n).
Sometimes, we refer to “
x
” as the
number of successes
and “
n  x
” as the
number o
failures.
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Rev.F08
6
The Sampling Distribution of the
Sample Proportion
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We already know we can make inferences about a
population mean
from
a
sample mean
.
Similarly, we
can make inferences about a
population
proportion
from a
sample proportion
.
To make inferences about a population mean, we must know the
sampling distribution of the sample mean
, that is the distribution of the
sample mean.
Thus, in order to make inferences about a population proportion, we
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 Summer '11
 Shaw

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