62 Estimating a Population Proportion
Two major applications of inferential statistics involve use of sample data to
1.
estimate the value of a population parameter, and
2.
test some claim (or hypothesis) about a population.
In this section we will learn to obtain a confidence interval in which a sample proportion
is used to estimate the value of a population proportion.
Assumptions
1.
The sample is a simple random sample.
2.
Conditions for a binomial distribution are satisfied
i.
There are a fixed number of trials
ii.
The trials are independent
iii.
There are two categories for outcomes, and
iv.
The probabilities must remain constant for each trial.
3.
The normal distribution can be used to approximate the distribution of sample
proportions because
and
are both satisfied.
5
np
≥
5
nq
≥
Notation for Proportions
p
=
Population
proportion
ˆ
x
p
n
=
=
sample
proportion of
x
successes
in a sample of size
n
.
ˆ
1
q
=−
ˆ
p
=
sample
proportion of
failures
in a sample of size
n
.
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 Spring '07
 Stone
 Statistics, Inferential Statistics, Normal Distribution, 90%, 51%, 2 95%, 16.9%

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