The concept
A confidence interval uses sample information to estimate a population quantity with an associated long-run coverage procedure. In the frequentist interpretation, a 95 percent method would cover the fixed true parameter in about 95 percent of repeated samples under its assumptions. It does not mean that 95 percent of individual observations fall inside the interval.
Worked example
A fictional archive randomly samples document handling times and estimates a mean of 12 minutes with a 95 percent confidence interval from 10 to 14 minutes. This expresses uncertainty about the population mean using the chosen method. It does not imply that nearly every document takes 10 to 14 minutes; individual cases may vary much more. The team separately examines the distribution of handling times for staffing decisions.
Limits and judgment
An interval can be narrow and still misleading if sampling is biased, records are dependent, or the statistical assumptions fail. More observations reduce some random uncertainty but do not automatically fix systematic errors. Report how the sample was collected and what quantity is being estimated, rather than presenting the interval as a universal guarantee of accuracy or coverage.
FROM UNDERSTANDING TO ACTION
Put it to work.
Explain the difference between an interval for average travel time and a range covering individual journeys.
RETRIEVE. REASON. REMEMBER.
Knowledge check.
Choose one answer for each question, then check your reasoning.
Sources & further reading.
Links support the core concepts or identify the book. Examples, exercises, and critical analysis are original Institute material. Source checks are not an independent expert review of every claim.
- NIST: Confidence Limits for the Mean ↗
Statistical core concept; all numerical scenarios and interpretations are original instructional examples. Source reviewed 2026-10-19.