difficulty 3/5
Confidence interval
A range built so that, across repeated experiments, a stated fraction of such ranges contain the true value. The fraction is a property of the method, not of the interval in front of you.
Intuition
You weigh nine gorillas and get an average of 90 kg. Report that number alone and you have implied a precision you do not have: weigh a different nine and you would get something else, purely because you weighed a different nine.
"Variation in the estimate caused by random selection is called sampling error" [1, §8.3], and the interval is how you report it. Interval estimates exist "because the estimate of the mean varies from sample to sample", and instead of a single number "a confidence interval generates a lower and upper limit" [2, §1.3.5.2].
The part almost everyone gets wrong is what the percentage attaches to. It is not a probability about your interval. It is a track record of the procedure, and both sources say so in nearly the same words.
Formal definition
How it works
Where it's used
Why & when
Worked example
Pitfalls
Check yourself
3 questions
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On the cheat sheet: Statistical testing →
Sources
- Think Stats, 2nd ed.book · retrieved 2026-09-06https://greenteapress.com/thinkstats2/html/index.html
- NIST/SEMATECH e-Handbook of Statistical Methodsstandard · retrieved 2026-09-06https://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm