In frequentist statistics, a confidence interval is defined by the long-run reliability of a sampling distribution rather than a probability statement regarding a specific realized interval containing a fixed parameter. The core principle asserts that if repeated random samples are drawn from a population and intervals constructed using the same method, approximately 95% of those calculated intervals will contain the true but unknown population mean; however, for any single computed interval, the parameter either lies within it or does not with zero probability. This concept belongs to inferential statistics specifically addressing estimation theory, distinguishing itself by treating parameters as fixed constants and sampling data as the source of variability, thereby contrasting fundamentally with Bayesian credible intervals which treat parameters as random variables governed by prior distributions.
In frequentist statistics, a confidence interval is defined by the long-run reliability of a sampling distribution rather than a probability statement regarding a specific realized interval containin…