8.1
Inference for a Single Proportion
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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View Full DocumentEX 1) A survey of 17,096 students in US fouryear colleges collected information on
drinking behavior.
The researchers defined “frequent binge drinking” as having five or
more drinks in a row three or more times in the past two weeks.
According to this
definition, 3314 students were classified as frequent binge drinkers. Compute the 95%
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 Fall '08
 ABDUS,S.
 Normal Distribution, 5%, consultant, 75%, 90%

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