Using an Applet to Demonstrate Confidence Intervals
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This page first made public: Feb 6, 2008
This material is replicated on a number of sites as part of the SERC Pedagogic Service Project
- Explain that confidence intervals are random quantities which vary from sample to sample and that they may miss the true population parameter.
- Explain that the confidence level is that proportion of possible samples for which the confidence interval will capture the true parameter.
- Given a study and confidence interval for the population proportion, describe how the following will affect the width of the confidence interval.
- Increasing the sample size
- Increasing the confidence level C
Context for Use
Before beginning, students need to be familiar with
- Given a confidence level C, determine the critical value (z*) from the standard normal table needed to construct the confidence interval.
- Construct a confidence interval for a population proportion using the formula.
Description and Teaching Materials
Teaching Notes and Tips
- It is very likely students will have different % coverage between their simulations of n=50 and n=100. Make sure to emphasize in class that this is due to sampling variability and not a change in the confidence level.
- Be sure to have students bring in their handout with results so that you can follow-up with a compilation of results.
- When the sample size changes from 50 to 100 the confidence level ________. From this we can conclude that the sample size _________ the confidence level. This way the students understand what they are expected to learn from the assignment.
- An optional addition to the in class discussion is to suggest to your students to go back and run a simulation of 1000 samples or higher so that they see that percent coverage settles around 95%.