Editing Interval estimation (section)

=== Confidence intervals ===
{{main|Confidence intervals}}

Confidence intervals are used to estimate the parameter of interest from a sampled data set, commonly the [[mean]] or [[standard deviation]]. A confidence interval states there is a 100γ% confidence that the parameter of interest is within a lower and upper bound. A common misconception of confidence intervals is 100γ% of the data set fits within or above/below the bounds, this is referred to as a tolerance interval, which is discussed below.

There are multiple methods used to build a confidence interval, the correct choice depends on the data being analyzed. For a normal distribution with a known [[variance]], one uses the z-table to create an interval where a confidence level of 100γ% can be obtained centered around the sample mean from a data set of n measurements, . For a [[Binomial distribution]], confidence intervals can be approximated using the [[Binomial proportion confidence interval|Wald Approximate Method]], [[Binomial proportion confidence interval|Jeffreys interval]], and [[Clopper-Pearson interval]]. The Jeffrey method can also be used to approximate intervals for a [[Poisson distribution]].<ref name=":0">{{Cite book |last=Meeker |first=William Q. |url=|title=Statistical Intervals: A Guide for Practitioners and Researchers |last2=Hahn |first2=Gerald J. |last3=Escobar |first3=Luis A. |date=2017-03-27 |publisher=Wiley |isbn=978-0-471-68717-7 |edition=1 |series=Wiley Series in Probability and Statistics |language=en |doi=10.1002/9781118594841}}</ref> If the underlying distribution is unknown, one can utilize [[Bootstrapping (statistics)|bootstrapping]] to create bounds about the median of the data set.