Confidence Interval Calculator
CI = mean ± z × (σ/√n). 90 / 95 / 99 % standard intervals.
Result
95% CI
[97.0600, 102.9400]
100 ± 2.9400.
- Sample mean100
- Std deviation15
- Sample size100
- Standard errorσ / √n1.500000
- Confidence level95%
- Critical z1.96
- Margin of error2.940000
- Lower bound97.060000
- Upper bound102.940000
Step-by-step
- SE = σ / √n = 15 / √100 = 1.5000.
- Margin = z × SE = 1.96 × 1.5000 = 2.9400.
- CI = mean ± margin = [97.0600, 102.9400].
How to use this calculator
- Enter sample mean and standard deviation.
- Enter sample size.
- Pick confidence level.
- Read CI bounds.
About this calculator
A 95% confidence interval means: if we repeated this sampling procedure many times, ~95% of CIs would contain the true population mean. Wider CI = less precision. Doubling sample size shrinks margin by √2 (~30%). Quadrupling halves margin. Common z-values: 80% → 1.282, 90% → 1.645, 95% → 1.96, 99% → 2.576. For small samples (n < 30), use the t-distribution instead — wider intervals at given confidence.
Frequently asked
Two views of the same statistical evidence. CI quantifies precision; p tests whether 0 (or some null value) lies in the CI.
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