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Sample Proportion

Let there be x successes out of n Bernoulli trials. The sample proportion is the fraction of samples which were successes, so

p^^=x/n.
(1)

For large n, p^^ has an approximately normal distribution. Let RE be the relative error and SE the standard error, then

<p>=p
(2)
SE(p^^)=sigma(p^^)=sqrt((p(1-p))/n)
(3)
RE(p^^)=sqrt((2p^^(1-p^^))/n)erf^(-1)(CI),
(4)

where CI is the confidence interval and erfx is the erf function. The number of tries needed to determine p with relative error RE and confidence interval CI is

n=(2[erf^(-1)(CI)]^2p^^(1-p^^))/((RE)^2).
(5)

See also

Sample

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Cite this as:

Weisstein, Eric W. "Sample Proportion." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SampleProportion.html

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