Confidence interval calculator

Frequently asked questions

What does a 95% confidence interval actually mean?

It means that if you repeated your sampling procedure many times and built an interval each time, roughly 95% of those intervals would contain the true population mean. It does not mean there is a 95% probability the true mean falls within this specific interval — the interval either contains it or it does not.

When should I use a t-distribution instead of a z-distribution?

A z-based interval is most appropriate when the sample size is large (often cited as 30 or more) or when the population standard deviation is known. For small samples or when population spread is uncertain, a t-distribution produces wider, more conservative intervals that better account for that uncertainty.

Why does a larger sample size produce a narrower interval?

Standard error — the spread of the sampling distribution — equals the sample standard deviation divided by the square root of sample size. As sample size grows, the denominator grows too, shrinking the standard error and pulling the interval bounds closer to the mean.

What confidence level should I use — 90%, 95%, or 99%?

Higher confidence requires a wider interval. A 95% level is the most common default in applied research. Use 99% when the cost of a wrong conclusion is high and you can tolerate a wider estimate. Use 90% when a narrower interval is more useful and a small miss rate is acceptable for your purpose.