SolveNook

Confidence Interval Calculator

Build a confidence interval from summary statistics using an explicit method. Choose Student t for an unknown population variance, normal mean intervals for a known population SD, or Wilson/basic normal intervals for a binomial proportion.

Mean-z requires a known population SD. Mean-t uses sample SD. Wilson is preferred to the basic normal proportion approximation at small counts. No finite population correction.

How the calculation works

Mean interval=mean±critical×SD/√n. Student t critical uses n−1 df. Wilson proportion uses its score-interval center and half-width; basic normal uses p±z√(p(1−p)/n).

Worked example

Mean 50, sample SD 10 and n=25 at 95% confidence gives a t interval approximately [45.8722,54.1278]. Twelve successes in twenty-five trials give a proportion estimate of 0.48.

Assumptions and limitations

Sample size at least two. Mean-z requires truly known population SD. Basic normal proportion intervals are not clipped and can be unreliable near 0/1 or at small counts. No finite-population or clustered-sample correction.

A confidence level describes repeated-sampling coverage under the method’s assumptions; it is not a probability assigned to a fixed parameter after seeing these data.

Sources and editorial responsibility

Maintained by Renvoro Pty Ltd. Sources inform the methods and assumptions shown here; outputs have the limitations described on this page.

Method reviewed 2026-10-13. Calculation standards · Report an issue