Confidence intervals for an average are not prediction intervals for the next case

A confidence interval estimates uncertainty about a parameter such as a population mean. In repeated sampling, a correctly specified 95% confidence procedure covers its target parameter in approximately 95% of repetitions. This does not mean that 95% of individual observations fall within that interval.

A prediction interval targets a future observation or a specified future aggregate. It includes uncertainty from future variation as well as uncertainty about the estimated parameter. Under the same normal independent-observation model, a prediction interval for one future case is therefore wider than the interval for the mean.

Illustrative example: the average duration of comparable workshops may be estimated quite precisely, while the duration of next week's individual workshop remains variable. A narrow interval for the average does not justify promising that every workshop will end within those bounds.

First state the target: overall average, next case, or average of several future cases. Then check distributional assumptions, dependence, and whether the future process resembles the observed one. A changed process can invalidate either calculation.

Evidence status: source-based synthesis. Examples are illustrative; no new experiment or independent outcome verification is claimed.