Confidence Interval Calculator
Inputs
Enter sample data and confidence level to calculate the confidence interval.
What is a Confidence Interval?
A confidence interval (CI) is a range of values that is likely to contain an unknown population parameter. It provides an estimate plus a margin of error.
For example, a 95% CI means that if you repeated the study many times, 95% of the calculated intervals would contain the true parameter.
Formulas
For a Mean:
CI = x̄ ± z × (σ / √n)For a Proportion:
CI = p ± z × √(p(1-p)/n)Common Confidence Levels
| Confidence Level | Z-Value |
|---|---|
| 90% | 1.645 |
| 95% | 1.96 |
| 99% | 2.576 |
Example
95% CI for a Sample Mean
x̄ = 50, σ = 10, n = 100
- ME = 1.96 × (10 / √100) = 1.96 × 1 = 1.96
- CI = 50 ± 1.96 = [48.04, 51.96]
Frequently Asked Questions
Why use 95%?
95% is a common standard in research. It balances precision with reliability. Higher confidence = wider interval.