Confidence Interval Calculator
Compute the Confidence Interval (CI) for mean estimates using Z-score or T-score methodology. Includes visualization of the margin of error and standard error.
About
A confidence interval defines the range within which a population parameter likely exists. Researchers use it to express the reliability of an estimate. A narrow interval suggests high precision while a wide interval indicates significant uncertainty. The calculation method depends on the sample size and whether the population standard deviation is known. For large samples we use the Z-distribution. For smaller samples under thirty we rely on the T-distribution which has heavier tails to account for added uncertainty.
Formulas
The general structure for the interval is point estimate plus or minus the margin of error.
Where s√n is the Standard Error.
Reference Data
| Confidence Level | Z-Score (∞ df) | T-Score (df=10) | Alpha (α) |
|---|---|---|---|
| 80% | 1.282 | 1.372 | 0.20 |
| 85% | 1.440 | 1.559 | 0.15 |
| 90% | 1.645 | 1.812 | 0.10 |
| 95% | 1.960 | 2.228 | 0.05 |
| 98% | 2.326 | 2.764 | 0.02 |
| 99% | 2.576 | 3.169 | 0.01 |
| 99.5% | 2.807 | 3.581 | 0.005 |
| 99.9% | 3.291 | 4.587 | 0.001 |