The new applet running below is designed to help students understand confidence intervals. Each of the 50 lines on the graph below represents a confidence interval for the mean (assuming known variance). Each interval is based on a sample of size 5 taken from a standard normal distribution (mean=0 and variance=1). By changing alpha, students can see how the confidence intervals are affected by this parameter. Also, students can get a good idea of what a confidence interval really means in terms of covering the true mean.
Pick an alpha for which a large number of confidence intervals are to be calculated by sliding the arrow along the alpha scale. When the desired value is found, simply click More Intervals!. Each time this button is clicked subsequently the default alpha level for a new set of 50 confidence intervals will be the value chosen. When clicking this button, be careful to wait and make sure the applet has performed all the necessary calculations before clicking it again. The first line of text allows you to see what intervals cover the true mean of 0 for the current set of 50 intervals as you change alpha. The second line of text gives the total number of intervals which have covered 0 at the default alpha level. By obtaining a total of 1000 confidence intervals, make statements about the coverage probability for the given value of alpha. I am not sure, however, how good the random number generator is right now.
Perform this simulation task for a wide range of alpha values. To change the default value, simply click New Alpha!, and slide the arrow along the alpha scale to the desired value of alpha and proceed with the steps above.