STAT 509 – Sections 4.4,4.8 – More Inference
• We can do inference (CIs, hypothesis tests) about
parameters other than a population mean.
Confidence Interval for a Proportion
• Suppose our data tell us only whether each
observation has a certain characteristic.
• We want to know how much of the population has that
characteristic.
• The proportion (always between 0 and 1) of
individuals with a characteristic is the same as the
probability of a random individual having the
characteristic.
Estimating proportion is equivalent to estimating the
binomial probability
p
.
Point estimate of
p
is the sample proportion
:
• Give every sampled individual a 1 (if it has the
characteristic) or 0 (if it lacks it).
Note
n
y
p
ˆ
is a type of sample average (of 0’s and 1’s),
so CLT tells us that when sample size is large, sampling
distribution of
p
ˆ
is approximately normal.
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n
:
100(1 –
)% CI for
p
is:
How large does
n
need to be?
Example 1:
We wish to estimate the probability that a
randomly selected part in a shipment will be defective.
Take a random sample of 179 parts, and find 14
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 Fall '08
 CHALMERS
 Normal Distribution, #, Fdistribution, 0.24585 liters

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