The Population Proportion
•
The population proportion is
p
(generally unknown).
•
The sample proportion is ¯
p
.
•
We use the sample proportion ¯
p
to estimate the population proportion
p
.
Example
: In a survey of 1500 American adults released on October 13, 2010,
46% of those questioned said they approved of the job Barack Obama is doing
as president.
We would also like to make conﬁdence intervals for the population propor
tion. In order to do this, we need to know the sampling distribution of the
sample proportion ¯
p
.
•
The expected value of the sampling distribution of ¯
p
is:
•
The standard error of the sampling distribution of ¯
p
is
σ
¯
p
:
•
The sampling distribution of ¯
p
will be approximately normal if
np
≥
5 and
n
(1

p
)
≥
5
.
1
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View Full DocumentExample
: A simple random sample of size 100 is selected from a population
with
p
= 0
.
40.
a. What is the expected value of ¯
p
?
b. What is the standard error of ¯
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 Fall '10
 Jager,AbigailL
 Normal Distribution, Standard Deviation, Standard Error, Variance

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