Title: Confidence Intervals | Brilliant Math & Science Wiki
Headings: Confidence Intervals
Confidence Intervals
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Rafael Del Valle Vega , Christopher Williams ,  and tlefacecat . contributed
A Confidence Interval is a region constructed using sampled data, of fixed size, from a population ( sample space) following a certain probability distribution. The interval is constructed to contain a chosen population statistic with prescribed probability. Simplified, the confidence interval is the probability that some value lies within a range. For example the value
μ
\mu μ, as in the statement: " given a sample of size
n
n n, assume a 95% confidence interval
( a, b)
(a, b) (a,b) is constructed to contain
μ
\mu μ ." This means that if all possible samples, of size
n
n n, from the population are considered, then 95% of the confidence intervals constructed from each of the samples will contain
μ
\mu μ. The fact that a confidence interval with certain probability has been constructed, does not guarantee that the interval constructed will contain the true statistic of the population. Just that, if the sample was chosen at random, then there is a 95% confidence (chance) that
( a, b)
(a, b) (a,b) contains
μ
\mu μ.