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

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

This formula produces the following image:

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