Take the following example for how t-distributions are put to use in statistical analysis. First, remember that a confidence interval for the mean is a range of values, calculated from the data, meant to capture a "population" mean. This interval is m +- t*d/sqrt(n), where t is a critical value from the t-distribution.2

For instance, a 95% confidence interval for the mean return of the Dow Jones Industrial Average (DJIA) in the 27 trading days prior to Sept. 11, 2001, is -0.33%, (+/- 2.055) * 1.07 / sqrt(27), giving a (persistent) mean return as some number between -0.75% and +0.09%. The number 2.055, the amount of standard errors to adjust by, is found from the t-distributio