How to Calculate a Confidence Interval
A confidence interval gives a range of values within which the true population parameter is likely to fall. A 95% confidence interval means that if you repeated the study 100 times, approximately 95 of the resulting intervals would contain the true population mean. Confidence intervals are fundamental to statistical inference and scientific reporting.
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Formula
Confidence Interval Calculator
Calculate the confidence interval for a population mean from sample data.
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Worked Example
Given:
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FAQs
What does a 95% confidence interval actually mean?
It means that 95% of all confidence intervals constructed from repeated samples of the same size would contain the true population parameter. It does not mean there is a 95% probability that the true mean falls within this specific interval — once calculated, it either does or does not.
How does sample size affect the confidence interval?
Larger samples produce narrower confidence intervals because the standard error (σ/√n) decreases as n increases. Doubling the sample size reduces the margin of error by a factor of √2 ≈ 1.41. This is why large surveys provide more precise estimates than small ones.
When should I use a wider confidence interval (99% vs 95%)?
Use 99% confidence intervals when the cost of being wrong is very high — medical studies, structural engineering, legal evidence. Use 95% for most research. The trade-off is that higher confidence requires a wider interval, which is less precise and sometimes less useful for decision-making.