Constructing confidence intervals to estimate a population
proportion
Submitted by gfj100 on Wed, 11/11/2009  12:45
NOTE: the following interval calculations for the proportion confidence interval is dependent on
the following assumptions being satisfied: np ≥ 10 and n(1p) ≥ 10. If p is unknown then use the
sample proportion.
The goal is to estimate p = proportion with a particular trait or opinion in a population.
•
Sample statistic =
(read "phat") = proportion of observed sample with the trait or
opinion we’re studying.
•
Standard error of
, where
n
= sample size.
•
Multiplier comes from this table
Confidence Level
Multiplier
.90 (90%)
1.645 or 1.65
.95 (95%)
1.96, usually rounded to 2
.98 (98%)
2.33
.99 (99%)
2.58
The value of the
multiplier increases
as the
confidence level increases
. This leads
to
wider
intervals for
higher confidence
levels. We are
more confident
of catching
the
population
value when we use a
wider
interval.
Example
In the year 2001 Youth Risk Behavior survey done by the U.S. Centers for Disease Control, 747
out of
n
= 1168 female 12
th
graders said they always use a seatbelt when driving.
Goal
: Estimate proportion always using seatbelt when driving in the population of all U.S.
12
th
grade female drivers.
Check assumption
: (1168)*(0.64) = 747 and (1168)*(0.36) = 421
both of which are at least 10.
Sample statistic is =
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 Spring '11
 AndyRegards
 Statistics, Confidence, confidence interval estimate

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