Education Technology

# Activities

40 Minutes

• ##### Device
• TI-Nspire™ CX CAS
• TI-Nspire™ CX
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

5.0

## Fair Go Penny

#### Activity Overview

What seems like a really simple coin tossing problem has a very surprising result that is counter intuitive.  After playing a few sample games students may start to become suspicious with regards to whether the game is fair. Students then start collecting data as evidence, leading to a great exploration that provides insights into sampling distributions, confidence intervals and Type I and Type II errors.

#### Objectives

The purpose of this activity is to encourage students to use data to validate whether or not the coin tossing game is biased. In using data, students need to consider sample size and the quantity of samples.

#### Vocabulary

• Sample
• Sampling distribution
• Type I and Type II error
• Confidence Interval

#### About the Lesson

This simple game is really not so simple! The results are counter intuitive. What seems like a fair game is indeed quite biased. Students run the simulations to see that the data supports the notion that the game is biased. Confidence intervals are treated informally through student 'certainty' with regards to the bias in the game. Type I and Type II errors are also treated informally, very relevant to all sorts of testing and statistics currently in the media.