Home Statistical Dictionary Confidence Interval

Confidence Interval

A range of values, computed from sample data, that would contain the true population parameter in a specified proportion of repeated samples.

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In Plain English

A 95% confidence interval doesn't mean there's a 95% chance the true value falls inside this particular interval. It means: if you repeated the whole sampling process many times and built an interval the same way each time, about 95% of those intervals would contain the true value.

Definition

For a parameter $θ$ and confidence level $1 - α$ , a confidence interval is an interval $[L, U]$ , computed from the sample, such that $P (L \leq θ \leq U) = 1 - α$ , where the probability is taken over repeated sampling -- $θ$ itself is fixed, not random, in frequentist inference.

Formula

\hat{θ} \pm z_{α /2} \cdot SE (\hat{θ})

Notation

\hat{θ}

—Point estimate of the parameter

z_{α /2}

—Critical value from the standard normal (or t) distribution

SE (\hat{θ})

—Standard error of the estimate

Properties

Increasing the confidence level widens the interval, all else equal.
Increasing the sample size narrows the interval, all else equal.
A frequentist CI says nothing about the probability of one specific interval containing $θ$ -- $θ$ is fixed, the interval is what's random.

At a Glance

Confidence levelcommonly 90%, 95%, or 99%

Width depends onsample size, variability, confidence level

Wider interval meansmore confidence, less precision

Not the same asa Bayesian credible interval

Related Terms

P-value Central Limit Theorem

Last updated July 30, 2026← Back to the Dictionary