General Formula for Confidence Intervals (1 of 2)
If a statistic is normally distributed and the standard error of the statistic is known, then a confidence interval for that statistic can be computed as follows:
statistic ± (z) (σstat)where σstat is the standard error of the statistic. For instance, the confidence interval for the mean is:
M ± z σM.where M is the sample mean and σM is the standard error of the mean. If the standard error has to be estimated then the formula uses t:
statistic ± (t) (sstat)where sstat is the estimated standard error of the statistic. For example, the confidence interval for the mean when σ is estimated is
M ± t sM.