Statistics Calculator

Confidence Interval Calculator

Calculate confidence intervals for population means from raw data or summary statistics.

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Confidence Level

Learning Guide

What is a Confidence Interval?

A confidence interval provides a range of values that is likely to contain the true population parameter. It quantifies the uncertainty in an estimate.

Formula for Mean CI

CI = x̄ ± z × (σ / √n)

x̄ = sample mean
z = z-score for confidence level
σ = standard deviation
n = sample size

Interpreting Confidence Intervals

A 95% CI means: If we repeated the sampling many times, 95% of the calculated intervals would contain the true population parameter.

Margin of Error

MOE = z × (σ / √n)

The margin of error is the "±" part of the confidence interval. Smaller margins indicate more precise estimates.

Factors Affecting Width

Higher confidence: Wider interval
Larger sample: Narrower interval
More variability: Wider interval

Common Confidence Levels

90%: z = 1.645 (less confident, narrower)
95%: z = 1.96 (standard, balanced)
99%: z = 2.576 (more confident, wider)