Click on the following links - please note these will open in a new window
In Chapter Eight, we introduced the notion of an inverse relationship between precision and confidence. That is, as a confidence interval gets narrower and consequently more precise, we can be less confident that the interval contains the true population parameter. Additionally, the material provided in Chapter 8 also highlighted the very important role of sample size in increasing the level of precision in our estimates.
The following exercise seeks to illustrate this relationship. Begin by navigating to the following URL: http://www.ruf.rice.edu/~lane/stat_sim/conf_interval/index.html. Click the "Begin" button at the upper left of your screen. A new window will have opened for you. Maximize this window. Read through the instructions provided to ensure you understand this simulation. With a sample size of 10 selected from the dropdown menu, click the "Sample" button. The graph to your left uses red and blue bars to show you which of the 100 confidence intervals generated do not contain the population parameter. Likewise, the cumulative results record this information.
Having run only one simulation thus far, which has generated 100 confidence intervals, click the "Sample" button 9 more times. Of the 1,000 confidence intervals you have now generated for a sample size of, note how many "Did Not Contain 50," the population mean. Record this information and set it aside.
Next, click the "Clear" button at the right of your screen. Now, use the dropdown menu and select 20 as your sample size. Click the "Sample" button 10 times. Once you have done so, note how many "Did Not Contain 50," the population mean. Compare this result to the result obtained for a sample size of 10. What do you notice? Do these results confirm the importance of sample size? If so, what is the evidence for this from the two simulations that you have run? If not, why not?