Is My Coin Fair?

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This activity is for an AP statistics class. Students design a coin and then perform an experiment and hypothesis test to see if it is fair or biased. Print Settings Printer Brand: MakerBot Printer: MakerBot Replicator Rafts: Yes Supports: No Resolution: standard Infill: 10% How I Designed This I used Tinkercad and designed a quarter. You can allow students to choose the type of coin and then look up dimensions. A quarter has a 24.26 mm diameter and a width of 1.75 mm. The cylinder can be shaped to that size and then decorated however students choose. I purposely did one side with an indentation and one side with letters popping out in hopes of showing this coin is unfair. Standards NGSS CCSS 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.