Wikipedia entry on Binomial Confidence Interval, Part 3

Steve Simon

2006-08-29

Categories: Blog post Tags: Wiki pages

[StATS]: Wikipedia entry on Binomial Confidence Interval, Part 3 (August 29, 2006). Category: Wiki pages

Here's some additional material that I will add to the Wikipedia entry on Binomial Proportion Confidence Interval.

An important theoretical derivation of these confidence intervals involves the inversion of a hypothesis test. Under this formulation, the confidence interval represents those values of the population parameter that would have large p-values if they were tested as a hypothesized population.

The normal approximation interval, for example, can be represented as

<math>\left \{ \theta; -Z_{\alpha / 2} \le \frac{{\hat p - \theta}}{{\sqrt{\theta p \left ( {1-\theta} \right ) / n}}} \le Z_{\alpha / 2} \right \}</math>

This formula produces the following image:

\\left \\{ \\theta; -Z\_{\\alpha / 2} \\le \\frac{{\\hat p -\\theta}}{{\\sqrt{\\hat p \\left ( {1-\\hat p} \\right ) / n}}} \\leZ\_{\\alpha / 2} \\right\\}{.tex}

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This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at

for pages similar to this one at with general help resources. You can also browse Children's Mercy Hospital website. Need more information? I have a page reproducing it here as a service, as it is no longer available on the Hospital. Although I do not hold the copyright for this material, I am This page was written by Steve Simon while working at Children's Mercy