If CI is the value of the confidence interval reported by the worksheet, the range of values between the sample mean minus CI and the sample mean plus CI is expected to include the true mean of the underlying population 95% of the time (for the 95% confidence interval) or 99% of the time (for the 99% confidence interval). This formula assumes that the data set is sufficiently large for the central limit theorem to apply.
95% Confidence Interval for the Mean
99% Confidence Interval for the Mean
where
tv,a = the value of the Student’s t distribution with v degrees of freedom such that difference between the cumulative probability function evaluated at tv,a and - tv,a is equal to 1- a.
SE = the standard error of the mean
See Also
Critical Value of K-S Statistic at 90%, 95%, and 99% Significance Level
Kolmogorov-Smirnov Goodness of Fit Statistic for Normal Distribution