MihsabaHow to use
A confidence interval summarizes uncertainty around a population parameter estimate. For a mean this tool uses Student’s t with the sample SD; for a proportion it uses the Wilson interval, which behaves better than the Wald interval near 0% and 100%.
- Choose mean or proportion.
- Select 90%, 95% or 99% confidence.
- Enter the appropriate sample statistics.
- Review estimate, bounds, standard error and critical value.
How it is calculated
Example
For sample mean 72, sample SD 15 and n=25 at 95% confidence, SE=3 and the tool uses a t critical value with 24 degrees of freedom.
Important notes
95% confidence does not mean there is a 95% posterior probability that this one computed interval contains the fixed parameter; it describes long-run coverage of the method across repeated samples. Check sampling assumptions for your context.
Frequently asked questions
When should I use t for a mean?
When the standard deviation comes from the sample, which is the usual case.
Why Wilson for a proportion?
It behaves better than the simple Wald interval, especially for small samples or proportions near 0 or 1.
Does higher confidence widen the interval?
Usually yes, because the critical value increases.
Is this calculator free?
Yes. It is free to use and requires no account.