In statistics, a confidence interval is a range of values that is determined through use of observed data, calculated at a desired confidence level, that may contain the true value of the parameter being studied. The confidence level, for example, a 95% confidence level, relates to how reliable the estimation procedure is, not the degree of certainty that the computed confidence interval contains the true value of the parameter being studied. The desired confidence level is chosen prior to the computation of the confidence interval and indicates the proportion of confidence intervals, that when constructed given the chosen confidence level over an infinite number of independent trials, will contain the true value of the parameter.
Confidence intervals are typically written as (some value) ± (a range). The range can be written as
an actual value or a percentage. It can also be written as simply the range of values. For example,
the following are all equivalent confidence intervals:
20.6 ±0.887
or
20.6 ±4.3%
or
[19.713 – 21.487]
\[ CI = X̄ ± Z * \frac{s}{\sqrt{n}}\]