Confidence Interval Simulation

Questions to be answered before the simulation are not yet implemented in this test version.


Begin by answering the questions, even if you have to guess. The first time you answer the questions you will not be told whether you are correct or not.


Once you have answered all the questions, answer them again using the simulation to help you. This time you will get feedback about each individual answer.


General Instructions


This simulation illustrates confidence intervals. For each run of the simulation, 100 sample experiments are conducted and a confidence interval on the mean is computed for each experiment. In each experiment, scores are sampled from a population with a mean of 50 and a standard deviation of 10. Therefore the parameter being estimated is always 50.


Both 95% and 99% confidence intervals are computed for each experiment. If the 95% confidence interval contains the population mean of 50, then the confidence interval is shown as an orange line. If the interval does not contain 50, it is shown as a red line. The 99% confidence intervals are shown by extending the 95% intervals. The extension is in blue if the 99% interval contains 50 and in white if it does not.


You can choose to make the sample size for each experiment 10, 15, or 20. One hundred simulated experiments are conducted when you click the “Sample” button. The cumulative results are shown at the bottom of the display. You can reset the cumulative results by clicking the “Clear” button.


Step By Step Instructions


1. Click the “sample” button and examine the 100 confidence intervals. Notice if any of them do not contain 50 (do not cross the black vertical line. Count the number of 95% intervals do not cross the line. Count the number of 99% intervals that do not cross the line. Compare your results to the tally shown at the bottom of the screen.


2. Push the “Sample” button several time and note the proportion of time the 95% and 99% confidence intervals do cross the line. Are these proportions similiar to the expected proportions of 0.95 and 0.99?


3. Notice whether the 95% or the 99% intervals are wider.


4. So far all your simulated experiments have been with sample sizes of 10. Change the sample size to 20. Test to see if this affects the widths of the confidence intervals. Also determne whether the proportion of the time the interval contains 50 is affected.


Summary


The 95% interval contains the parameter in question (the population mean of 50 in this case) 0.95 of the time. Naturally, the interval does not contain the parameter 0.05 of the time. The 99% interval contains the parameter 0.99 of the time.


The 99% interval is wider than the 95% interval. The larger the sample size, the shorter the interval. Sample size does not affect the proportion of the time the interval contains the parameter.