Confidence interval

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Informally, in frequentist statistics, a confidence interval (CI) is an interval which is expected to typically contain the parameter being estimated. More specifically, given a confidence level ${\displaystyle \gamma }$ (95% and 99% are typical values), a CI is a random interval which contains the parameter being estimated ${\displaystyle \gamma }$% of the time.^[1][2] The confidence level, degree of confidence or confidence coefficient represents the long-run proportion of CIs (at the given confidence level) that theoretically contain the true value of the parameter; this is tantamount to the nominal coverage probability. For example, out of all intervals computed at the 95% level, 95% of them should contain the parameter's true value.^[3]

Factors affecting the width of the CI include the sample size, the variability in the sample, and the confidence level.^[4] All else being the same, a larger sample produces a narrower confidence interval, greater variability in the sample produces a wider confidence interval, and a higher confidence level produces a wider confidence interval.^[5]