## Thursday, March 1, 2018

### Teach 180: Is the Coin Fair? (Day 115)

Although students can spout off what Type I and Type II errors are for hypothesis testing, they often have trouble understanding what would lead to making this type of error.  Today I gave them information on two coins.  Students had to determine if the coin was fair or not.  The null hypothesis corresponded to the fair coin and the alternative hypothesis corresponded to the unfair coin.  What would you conclude about Coin 1 - fair or unfair?  What would you conclude about Coin 2 - fair or unfair?

FLIPPING RESULTS FOR COIN 1

FLIPPING RESULTS FOR COIN 2

I had students discuss this in groups and one group of students couldn't decide.  They thought both coins were fair.  So, I asked them to look at the 95% confidence intervals.  If they could only choose one coin to use for the NFL Superbowl coin toss, which one would it be?  They said Coin 2.  The confidence interval contains .50 and the proportion of heads is closer to 50% than the other coin.

The big reveal came when they flipped the papers over.  Coin 1 was actually the fair coin and Coin 2 was actually the unfair coin.  With Coin 1 they had made a Type I error and with Coin 2 they had made a Type 2 error.

We'll see if this helps student understanding when they have their test next Friday - the day before Spring Break!  (NOTE: I created this simulation in Fathom and kept re-randomizing until I made errors for both the fair and the unfair coin.  If you would like a copy of this Fathom file, let me know in the comments below or send me an email to leighnataro@gmail.com.)