Using an Applet to Demonstrate Confidence Intervals

This page authored by Pam Arroway, Jennifer Gratton, Steve Stanislav, and Roger Woodard, North Carolina State University, based on an applet by Dr. Sundar Dorai-Raj, Virginia Tech.
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This material is replicated on a number of sites as part of the SERC Pedagogic Service Project


Students work individually with an applet to enhance their understanding of confidence intervals. Using a detailed step by step activity, they will use simulated data from the applet to determine the percentage of confidence intervals that capture the population proportion.

Learning Goals

Students should be able to:
  • 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

This activity is appropriate for a college introductory statistics course for any class size. This can be done in a lab setting or as an out-of-class assignment.
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

Student Handout (Microsoft Word 141kB Aug14 06)

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.


Make sure to emphasize in class the following day:
  • 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%.

References and Resources