What is a Confidence Interval?
A confidence interval is a statistical measure used to indicate the range of estimates within which an unknown statistical parameter is likely to fall. If the parameter is the population mean, the confidence interval is an estimate of possible values of the population mean.
A confidence interval is determined through use of observed (sample) data and is calculated at a selected confidence level. The confidence level indicates the reliability of the estimation procedure. Confidence intervals are typically written as (some value) ± (a range), where the range is known as the margin of error.
Meaning of "Confidence Level"
A 95% confidence level indicates that if 100 confidence intervals were computed across 100 independent trials, it is expected that 95 of these intervals will contain the true value of the given parameter. It does not say anything about the probability of a specific confidence interval containing the true value—the selected interval will either contain it or it will not. This is a common statistical misconception.
Formula Terms
- X̄ (Sample Mean)The average of your sample
- ZZ-value for the chosen confidence level
- σ or sPopulation or sample standard dev.
- nSample size (amount)
Calculating Confidence Intervals
This calculator computes confidence intervals for normally distributed data with an unknown mean, but known standard deviation. It assumes that the population standard deviation is known or that the sample size is large enough (n > 30) such that the sample standard deviation is a suitable approximation.
The expression Z × (σ / √n) represents the Margin of Error.
Common Z-values for Confidence Levels
The Z-value is critical for defining the bounds of the interval. Below are the standard normal Z-values used for various desired confidence levels:
| Confidence Level | Z Value |
|---|---|
| 70% | 1.036 |
| 80% | 1.282 |
| 90% | 1.645 |
| 95% (Most Common) | 1.960 |
| 98% | 2.326 |
| 99% | 2.576 |