8.1
Inference for a Single Proportion
recall from 5.1, when n is large:
p
ˆ
~ N (p,
n
p
p
)
1
(

)
Largesample confidence interval for a population proportion
Choose an SRS of size
n
from a large population with unknown proportion
p
of
successes.
The sample proportion
is:
p
ˆ
=
n
X
where
X
is the number of successes.
The standard error
of
p
ˆ
is:
p
SE
ˆ
=
n
p
p
)
ˆ
1
(
ˆ

and the margin of error for confidence level C is:
m
=(
z
*)(
p
SE
ˆ
)
where
z
* is the value for the standard normal density curve with area C between –
z
* and
z
*.
A approximate level C confidence interval for
p
is
p
ˆ
±
m
Use this interval for 90%, 95%, or 99% confidence when the number of successes and the
number of failures are both at least 15.
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Example 1
USA Today polled registered voters in the US and asked, “Do you support President
Obama?”
Of the 1000 individuals who were polled, 620 responded, “Yes.”
Compute the
95% confidence interval for
p
, the proportion of all registered voters in the US who
support President Obama.
Largesample significance test for a population proportion
Draw an SRS of size
n
from a large population with unknown proportion
p
of successes.
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 Spring '08
 ABDUS,S.
 Normal Distribution, Senator Smith

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