Park City Mathematics Institute
Reasoning from Data and Chance
Drafts of Project Files (password required)
- Which is the Better Guess?
- Jocelyn Co, Laurie Conley*, Patrick Phippen
- Students will run a simulation (using Fathom software) to decide if always choosing the same letter when guessing on a standardized multiple choice test will result in more "correct" answers (and a higher grade) than using random letters for each problem.
- Joker is Wild
- Antonio Baccay, Nathan Dummitt*
- This is a lesson plan for a classroom using Fathom statistical software. The lesson plan is split into three modules. The first module is appropriate for students who have had little or no experience with basic statistics and probability. Module 2 contains slightly more advanced activities for students who have had exposure to elementary statistics and probability. Finally, Module 3 compares the histogram of a given sample to the histogram of the sample repeated n times, and is appropriate for intermediate statistics students who are familiar with sampling distribution. Students will use Fathom software to simulate an experiment in order to answer a question about the basic probability of card shuffling using conditional operations in Fathom.
- Experimental to Theoretical
- Kymberly Riggins
- For enough trials, the experimental probability approaches the theoretical probability. The question arises, "How much is enough?". The students will each randomly generate answers for a test. Different groups will have different numbers that will represent the number of test questions on the test. The students will run fathom to see after how many trials will the mean of the experimental probability reach an appropriate error distance of the theoretical probability for a considerable length of time.
- Biased Multiple Choice
- Camilla Perkes
- This individual or group activity requires students to test randomly generated multiple choice tests from the same author to determine whether the author is biased towards a certain correct answer. Students will use Fathom to collect measures on these tests and adjust the number of tests generated to detect the bias. Students will engage in small group discussions to justify their interpretation of the data they collect.
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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.