All AP Courses

Lab

Is This Coin Fair?

Each round hands you a coin that is either fair or secretly biased. You choose how many times to flip it and what significance level to use. The lab runs the one-proportion z-test with you, then reveals the truth. Over many rounds you will see exactly where Type I and Type II errors come from.

Challenges

  1. Play 10 rounds with 20 flips each, then 10 rounds with 200 flips. Which setting caught more biased coins?
  2. Use a significance level of 0.01, then 0.10. Which setting produced more Type I errors over 20 rounds?
  3. Explain in context what a Type II error means for this game.
  4. Find a round where the p-value was small but the coin was fair. What is the name for that outcome?

Topics this lab supports