# Reese's Pieces Activity: Sampling from a Population

as part of its collaboration with the SERC Pedagogic Service.

## Summary

This activity uses simulation to help students understand sampling variability and reason about whether a particular sample result is unusual, given a particular hypothesis. By using first candies, then a web applet, and varying sample size, students learn that larger samples give more stable and better estimates of a population parameter and develop an appreciation for factors affecting sampling variability.

First, students estimate the proportion of orange Reese's pieces in a random sample of 25 candies. Students then use an actual sample of Reese's pieces candy to calculate a sample proportion, and then compare results for different samples, taken by each student in the class. Next, students will use the Web Applet Reese's Pieces (at rossmanchance.com) to gather information on the sample proportions of orange candies in random samples of 25. During this stage of the activity students will compare their group and the class results to the actual parameters. In the final part of the activity, the students will use the Applet to investigate the effect of sample size on correctly estimating parameters.

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## Learning Goals

## Context for Use

### Pre-instructional Decisions

Materials:- One Dixie cup per group (each with 40 Reeses Pieces in it)

- Reeses Pieces (enough for 40 per group)

- Reeses Pieces Web Applet - URL: www.Rossmanchance.com/applets/Reeses/ReesesPieces.html (see Available Technologies)

## Description and Teaching Materials

This activity takes place over three stages. The following sections give the lesson details and are to be used with a student handout. (Copy of Student Handout) (Microsoft Word 93kB Feb25 07)

### Stage One of Activity: Studying the variability of orange candies

### Stage Two of Activity: simulating samples using an applet

### Stage Three of Activity: studying the effect of sample size

## Teaching Notes and Tips

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## Assessment

Here are some questions that can be given to students to discuss or write answers to:

## References and Resources

Rossman, A. J., & Chance, B. L. (2000). Workshop Statistics: Discovery with Data, 2nd Edition. Key College Publishing.

Garfield, J., & Ben-Zvi, D. (in preparation) Developing students statistical reasoning connecting research and teaching practice. Key College Press