Performance of a WS 95% confidence interval when estimating the mean of a simulated normal distribution. Each sample size was tested with 100,000 samplings from the simulated population. (A) Simulated population parameters. (B) The percent of 95% confidence intervals that include the known population mean. The interval performs close to the nominal value. (C) Width of confidence interval (precision) relative to sample size. The black line indicates the average width of the confidence interval. Dotted lines bound the confidence interval width of 95% of trials. The red line shows the 95% a priori precision displayed as fractions of SDs. The inset shows example trials and confidence intervals relative to the sampled population. (D) The confidence intervals that do not include the population mean (∼5%) still approach the population mean as sample size increases. Traces are for trials where the confidence interval did not include the simulated population mean. The black line is the average distance of the population mean to the nearest boundary of the confidence interval. The dotted line is the distance between the population mean and the confidence interval that includes 95% of trials.