The sample proportion for 
successes out of 
Bernoulli trials is the
fraction of samples that were successes, so
 |
(1)
|
For large 
,
has an approximately normal
distribution. Let RE be the relative error
and SE the standard error, then
 |  |  |
(2)
|
 |  |  |
(3)
|
 |  |  |
(4)
|
where CI is the confidence interval and 
is the erf
function. The number of tries needed to determine 
with relative error RE and
confidence interval CI is
![n=(2[erf^(-1)(CI)]^2p^^(1-p^^))/((RE)^2).](/images/equations/SampleProportion/NumberedEquation2.svg) |
(5)
|
