Calculate the confidence interval for a population mean using sample data — choose from 90%, 95%, 99%, or a custom confidence level. Shows margin of error, z-critical values, and interpretation.
Sample Parameters
95% Confidence Interval
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Lower Bound
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Upper Bound
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Margin of Error
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Z-critical
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Enter sample parameters above
CI = x̄ ± z* × (σ/√n) — interval likely containing the true population mean.
Frequently Asked Questions
What does a 95% confidence interval mean?
A 95% CI means that if you repeated the sampling process many times, 95% of the resulting intervals would contain the true population parameter. It does NOT mean there is a 95% chance the true mean is in THIS specific interval.
When should I use a t-distribution instead of z?
Use the t-distribution when the population SD is unknown and the sample is small (n < 30). Use the z-distribution when the population SD is known, or n ≥ 30 (Central Limit Theorem applies).