A confidence interval is a range of values, derived from sample statistics, which is likely to contain the value of an unknown population parameter. Because of their random nature, it is unlikely that two samples from a given population will yield identical confidence intervals. But, if you repeat your sample many times, a certain percentage of the resulting confidence intervals will contain the unknown population parameter. The percentage of these confidence intervals that contain the parameter is the confidence level of the interval.

For 95% confidence intervals, an average of 19 out of 20 contain the population parameter.

Most frequently, you’ll use confidence intervals to bound the mean or standard deviation, but you can also obtain them for regression coefficients, proportions, rates of occurrence (Poisson), and for the differences between populations.

Suppose you have a 95% confidence interval of [5 10] for the mean. You can be 95% confident that the population mean falls between 5 and 10.

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