Is My Coin Fair?

thingiverse

This activity is designed for an AP statistics class, where students create a coin and then conduct an experiment to determine if it's fair or biased using a hypothesis test. I used Tinkercad to design a quarter with specific dimensions: 24.26 mm in diameter and 1.75 mm wide. Students can use these dimensions or choose their own coin type, researching its measurements online. I deliberately designed one side with an indentation and the other with raised letters to show that this coin is unfair. Standards Covered: * NGSS (Next Generation Science Standards) * CCSS (Common Core State Standards) Overview and Background Project: Is My Coin Fair? This project helps students practice performing a Chi-Square Goodness of Fit test. By designing and testing their own coins, students will learn about fair and biased coins. Objectives: * Students will understand what makes a coin fair or unfair. * After seeing the results, they'll be able to identify which coins were designed to be fair and which were biased. Standards Covered: * Students practice performing a Chi-Square Goodness of Fit test. Lesson Plan and Activity First, students design a coin using standard coin dimensions. Next, they answer questions about running a hypothesis test, such as the null and alternative hypotheses, degrees of freedom, and critical value. Once their coin is printed, they'll perform an experiment by flipping it 50 times, then calculate the test statistic to conclude if their coin was fair or biased. Optional Extension: * Design a fair coin or try to design a biased coin. * Run through the hypothesis test again. Skills Learned: * Chi-Square Goodness of Fit Test * Duration of Lesson This activity can take one day with multiple printers, but if there's only one printer or you do the extension, it may need to be split into two days due to print time. Preparation should include prior knowledge of hypothesis testing and the Chi-Square Goodness of Fit test. Rubric and Assessment Here is a sample rubric for the worksheet: Question (points) 1. 1 2. 1 3. 1 4. 1 5. 1 6. 1 7. 3 Making the coin: 1 Total: 10 points References For additional learning or review, students can watch Khan Academy videos on the Chi-square distribution and goodness of fit test: https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/chi-square-distribution-introduction