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:
This work is licensed under a Creative Commons Attribution 3.0 United States License. It was written by Steve Simon and was last modified on 04/01/2010.
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