Title: Sample Proportion -- from Wolfram MathWorld
Open Graph Title: Sample Proportion -- from Wolfram MathWorld
X Title: Sample Proportion -- from Wolfram MathWorld
Description: 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 (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...
Open Graph Description: 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 (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...
X Description: 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 (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...
Opengraph URL: https://mathworld.wolfram.com/SampleProportion.html
Domain: mathworld.wolfram.com
| DC.Title | Sample Proportion |
| DC.Creator | Weisstein, Eric W. |
| DC.Description | 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 (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... |
| DC.Subject | Mathematics:Probability and Statistics:Trials |
| DC.Rights | Copyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement. |
| DC.Format | text/html |
| DC.Identifier | https://mathworld.wolfram.com/SampleProportion.html |
| DC.Language | en |
| DC.Publisher | Wolfram Research, Inc. |
| DC.Relation.IsPartOf | https://mathworld.wolfram.com/ |
| DC.Type | Text |
| og:image | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_SampleProportion.png |
| og:type | website |
| twitter:card | summary_large_image |
| twitter:image:src | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_SampleProportion.png |
| None | ie=edge |
Links:
Viewport: width=device-width, initial-scale=1