## Quick Reference

A statement about the likely value of a future observation. It has a similar interpretation to a confidence interval but the interval is wider because it allows for the random error associated with the future observation.

For example, if a random sample of *n* observations is taken from a population with known variance *σ*^{2} and unknown mean *μ*, then the natural estimate of *μ* is *x̄*, the sample mean. A confidence interval for *μ* is based on the uncertainty in the estimate, which has variance *σ*^{2}/*n*. However, associated with a future observation from this distribution is the future random sampling variation with variance *σ*^{2}. A prediction interval for a future observation is based on the sum of the two variances, *σ*^{2}+*σ*^{2}/*n*.

*Subjects:*
Probability and Statistics.

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