Overview and Background

Project: Is My Coin Fair?

Students will get practice performing a Chi-Square Goodness of Fit test.

Objectives

Students will learn what a fair coin is and, after seeing everyone’s coin and results, get a feel for which coins were designed to be fair and which were biased.

Standards

Students get practice performing a Chi-Square Goodness of Fit test.

Lesson Plan and Activity

First, students will design a coin, using the standard size of a quarter, nickel, dime, or penny. Next, they will answer questions about running a hypothesis test, such as what the null and alternative hypotheses are, the degrees of freedom, and the critical value. Once the coin is finished printing they will perform an experiment by flipping it 50 times. They will then calculate the test statistic and conclude if their coin was fair or biased. There is an optional extension to have students try to design a fair coin or try to design a biased coin and then run through the hypothesis test again.

Skills Learned

Chi-Square
Fit Test

Duration of Lesson

This activity can take one day if you have enough printers available to students. The print time for my quarter sized coin was 9 minutes. If there is only one printer or if you do the extension, you may need to split it into two days to allow for printing time.

Preparation

Students should have already learned hypothesis testing including the Chi-Square Goodness of Fit test.

Rubric and Assessment

Here is a sample rubric to use with the worksheet.
Question (points)
1 (1)
2 (1)
3 (1)
4 (1)
5 (1)
6 (1)
7 (3)
Making the coin (1)
Total 10

References

If you would like to have students learn or refresh their memory on the Chi-square distribution and how the goodness of fit test works they can watch the Khan Academy videos on these topics.

https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/chi-square-distribution-introduction.