12.3 Inference on Population Proportion
•
We use proportions when we have qualitative data.
•
If we have qualitative data, all we can do is count the number of
occurrences of each value.
From the counts we calculate proportions.
•
For example, if we ask consumers of a particular product which brand
they prefer (A, B, C or D), numbers are arbitrary: can’t calculate mean
or variance.
So, maybe the manufacturers of brand A want to know something
about the proportion of the pop who prefer their brand.
In that case, we count how many people chose brand A out of how
many people we asked.
The people who chose
brand A are labeled ‘successes’ and all others
are ‘failures’.
•
The logical statistic to use to estimate and test the population
proportion would be the sample proportion.
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So, we take a sample and calculate the sample proportion
.
ˆ
x
p
n
=
The sampling distribution of phat is approximately normal if our
n
is large
enough, so we can use the Z table.
To check to see if our
n
is large enough,
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 Spring '08
 CathyDavis
 Statistics, Statistical hypothesis testing, Leno

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