Click on the "One Sample" button to generate a random sample from a normal distribution with mu = 100 and sigma = 15 and to see the details of calculating the confidence interval for the population mean from that sample. Do this a few times until you understand the process. Then click on the "10 Samples" button to see the confidence intervals for 10 samples. Finally, click on the "100 Samples" button to see 100 confidence intervals displayed at once. These are 95% confidence intervals, so about 95% of the confidence intervals should include the true population mean. Do they?
In the applet below, follow the same procedures, this time calculating 99% confidence intervals.
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