Calculate the confidence interval for a population mean
This confidence interval calculator estimates the range within which a population parameter is likely to fall, given a sample statistic and a chosen confidence level. It uses the standard error of the mean and the z-critical value for the selected confidence level to compute the margin of error.
Where x̄ is the sample mean, z is the z-critical value, σ is the population standard deviation, and n is the sample size.
If you were to repeat the sampling process many times, approximately 95% of the computed confidence intervals would contain the true population mean. It does not mean there is a 95% probability that the true mean lies within the interval.
Use a z-interval when the population standard deviation is known and the sample size is large (n ≥ 30). Use a t-interval when the population standard deviation is unknown and you must estimate it from the sample.