# Confidence Interval Calculator: Results in Real Time
The Confidence Interval Calculator instantly computes the interval, margin of error, critical value, and standard error. It supports Z distribution (known population sigma) and Student t (sample sigma), with any confidence level between 0 and 100. 2 Z and t Distributions
Live Real-Time Results
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# Z Distribution vs Student t
| Criterion | Z Distribution | Student t |
|---|---|---|
| When to use | Known population σ or n > 30 | Sample s, any n |
| Critical value (95%) | z* = 1.960 | t* depends on df = n−1 |
| Degrees of freedom | Not applicable | df = n − 1 |
| For large n | Narrower CI | Converges to Z |
How to Correctly Interpret a Confidence Interval
A 95% confidence interval does not mean there is a 95% probability that the true mean lies in that specific interval. It means the procedure, if repeated with many samples, would produce intervals containing the true mean 95% of the time. Once computed, the interval either contains the true value or it does not.# Quick Reference Glossary
- Confidence Interval (CI)
- Range [x̄ − ME, x̄ + ME] estimating the population parameter at the chosen confidence level.
- Confidence Level
- Proportion of intervals that would contain the true parameter if the experiment were repeated many times. Typical values: 90%, 95%, 99%.
- Standard Error (SE)
- SE = σ/√n. Measures the variability of the sample mean around the population mean.
- Margin of Error (ME)
- ME = z* × SE (or t* × SE). It is the half-width of the confidence interval.