This applet uses the Student's t distribution to construct confidence intervals for the mean of a non-normal (Gamma) population. By varying the amount of departure from normality, the effect of violating the assumption of normality can be studied.
How to use the applet
- Specify the parameters of the Gamma distribution, r and
, in the left pane of the applet. Note, these cells act like a spreadsheet application; to
change an entry, click on it, delete the current value, type a
new one, and then press enter. The applet plots the Gamma distribution and its normal approximation.
- Specify a level 100(1 - alpha)% confidence interval and click the Regenerate button. The applet generates 10,000 samples of of size 5 from the specified Gamma distribution. For each sample, the applet computes the sample mean, sample standard deviation, lower and upper confidence limits for the specified level, and whether the confidence interval covers the true mean. At the bottom, the applet presents the coverage probability.
The applet