An In-Class Experiment to Estimate Binomial Probabilities
This material is replicated on a number of sites as part of the SERC Pedagogic Service Project
This hands-on activity is appropriate for a lab or discussion section for an introductory statistics class, with 8 to 40 students. Each student performs a binomial experiment and computes a confidence interval for the true binomial probability. Teams of four students combine their results into one confidence interval, then the entire class combines results into one confidence interval. Results are displayed graphically on an overhead transparency, much like confidence intervals would be displayed in a meta-analysis. Results are discussed and generalized to larger issues about estimating binomial proportions/probabilities.
Context for Use
Description and Teaching Materials
- Intervals based on n = 100 have different centers but are all about the same width. (Note that if you use something with a true p reasonably close to .5, the half-width of the intervals will be about 0.1.)
- Intervals based on n = 400 have different centers, but are all about the same width and are half as wide as those with n = 100.
- The interval based on the entire class is narrow and provides a more accurate estimate of p than the individual intervals.
- The larger your sample size, the more accurately you can estimate a parameter.
There are three files to download. Two of them are provided in pdf and Word format. The pdf file is provided to make sure users can see the correct page layout. The Word files are provided so that users can modify the files. The first file contains detailed instructions for the teacher, including logistical issues and discussion questions. The second file is to be handed out to each team, with instructions for the students and spaces to record their results. The third file is the grid for recording the results, which should be printed onto an overhead transparency.
Instructions for the Instructor:
Instructor Instructions as pdf file (Acrobat (PDF) PRIVATE FILE 115kB May17 07) Instructor Instructions as Word file (Microsoft Word PRIVATE FILE 46kB May17 07)
Team Record Sheet to be handed out to students:
Student Team Record Sheet as pdf file (Acrobat (PDF) PRIVATE FILE 74kB May17 07) Student Team Record Sheet as Word file (Microsoft Word PRIVATE FILE 34kB May17 07)
Grid for overhead transparency to record results:
Grid for Overhead transparency (Microsoft Word PRIVATE FILE 124kB May3 07)
The activity as described uses "animal eyes." These are plastic pieces used to glue onto a stuffed animal, which have a flat side and a curved side that looks like an eye. They can be purchased in a craft shop or online (type "animal eyes craft" into a search engine). The goal is to have a binomial situation for which the success probability is unknown. The animal eyes can be flipped and a "success" is that the eye lands looking up. You could use a different binomial experiment, such as estimating the proportion of one color in a multi-colored candy. The important criteria are that the experiment mimics a binomial setting, that each student can get an individual result with n = 100 trials, and that it makes sense to combine the results across students.
Teaching Notes and Tips
The hardest part of this activity is reconvening the class when they have completed the experiment, and holding a discussion about the process and concepts. One possibility is to have students discuss the relevant questions in their teams, then report back to the class.
References and Resources
- Activity-Based Statistics Richard L. Scheaffer, Mrudulla Gnanadesikan, Ann E. Watkins, and Jeffrey Witmer, Revised by Tim Erickson, Key Curriculum Press.
- Workshop Statistics: Discovery with Data, 2nd Edition, Allan J. Rossman and Beth L. Chance, Key Curriculum Press
- Mind On Statistics (2006), Jessica Utts and Robert Heckard, Duxbury/Brooks-Cole