The interactive WISE Confidence Interval Creation Applet allows instructors to demonstrate how sample size, alpha level, population shape, and variance affect confidence intervals. The user can generate a population distribution of interest or select a distribution from a menu, select a sample size and an alpha level.
A press of the 'Sample' button displays a simulated sample and confidence interval for the population mean. The sample mean, standard deviation, and confidence interval are displayed, along with the option to display calculations for the confidence interval limits. Subsequent presses of the 'Sample' button produce new random samples with their associated confidence intervals. Up to 20 confidence intervals are displayed at one time, showing how confidence intervals differ by chance.
This applet provides graphic evidence for why it is wrong to say that the population mean falls within a given confidence interval 95% of the time. Rather, 95% of confidence intervals are expected to contain the population mean IF assumptions are met. Manipulations of the population shape and the sample size easily produce situations where the assumption of normality is violated to an extent where standard procedures for constructing confidence intervals are clearly wrong. Students and instructors can have fun playing with the applet and interpreting findings.
The applet is linked to a demonstration guide.
