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This applet simulates sampling from a population with a mean of 50 and a standard deviation of 10. For each sample, the 95% and 99% confidence intervals on the mean are computed based on the sample mean and sample standard deviation. The intervals for the various samples are displayed by horizontal lines as shown below. The first two lines represent samples for which the 95% confidence interval contains the population mean of 50. The 95% confidence interval is orange and the 99% confidence interval is blue. In the third line, the 95% confidence interval does not contain the population mean; it is shown in red. In the seventh and last line shown below, the 99% interval does not contain the population mean; it is shown in white.
Specify whether you want the sample size to be 10, 15, or 20 scores and click the "Sample" button. Then, 100 samples of the specified sample size will be taken and the resulting 100 confidence intervals will be plotted.
The cumulative number of confidence intervals containing and not containing the population parameters is tallied.
In this simulation, you know that the population mean is 50. Naturally, a researcher will not know the value of the population mean and that is why he or she collects a sample of data. While the simulation shows thousands of samples, a researcher typically has only one sample. In the simulation we can see whether a confidence interval contains the population mean or is one of the unfortunate few that misses the population mean. But in practice we do not know whether the single confidence interval that we compute captures the population mean or is one of the unlucky few that does not. The simulation shows us the variation in the sample mean, from sample to sample, and helps to illustrate how confidence interval width depends on the sample size and the confidence level.
The simulations were developed as part of a grant from NSF to David Lane of Rice University. Partial support for this work was provided by the National Science Foundation's Division of Undergraduate Education through grant DUE 9751307. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.