# Confidence Interval

## Confidence Interval

A confidence interval makes it possible to define a margin of error between the results of a survey and an exhaustive summary of the entire population.

More generally, the confidence interval makes it possible to assess the precision of the estimate of a statistical parameter on a given sample.

### Example

Consider E = {x1,…, xn} a sample of a distribution of a random variable.

• We’re interested in one particular event of this random variable and in one estimation x of the value of this parameter. If it is possible to determine this estimate by a segment so that we can confirm that this segment contains the exact value of the estimate with a given probability p, then we call this segment a confidence interval associated with the estimate under consideration.
• The bounds of this interval are random variables that only depend on the sample. The length of the confidence interval is a measure of the uncertainty of the real position of the true value of the event under consideration.
• The determination of the confidence interval of an event or of the parameter of a random variable involves mathematical tools that go beyond the more restricted context of this glossary.