# Confidence Intervals, Confidence Levels, and Average Interval Length

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A confidence interval for estimating a parameter of a probability distribution must show two basic properties. First, it must contain the value of the parameter with a prescribed probability (the "confidence level"), and second, it must be as narrow as possible in order to be useful. Confidence intervals may be constructed in several ways, although in practice it is usually not possible to attain precisely the desired confidence level, contrary to common belief. This is illustrated in the present Demonstration for a binomial distribution with trials and probability parameter .

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Contributed by: Tomas Garza (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The article on Binomial proportion confidence interval* *in Wikipedia gives the details for Wilson's method. Implementation of the Clopper–Pearson method is due to the author of this Demonstration.