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.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentSo, 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
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 CathyDavis
 Statistics, Statistical hypothesis testing, Leno

Click to edit the document details