I have the luxury, nay, the honor, of teaching the high school varsity kicker in my statistics class. He’s been talking about how good he is, and I wanted to give him the chance to show off. We are learning how to run significance tests for proportions and I decided to take a different approach in how we addressed the topic. I didn’t tell my students about what new significance test we were learning, rather, I just gave them this:
The kicker’s picture has been removed for obvious reasons. The slide did not have any of the writing on it; we added that as needed during the lesson. I asked my students how we could answer who was a better kicker. The first thing they decided was that they needed to see our kicker in action.
I asked him to kick ten field goals from 40 yards. 9 out of 10 isn’t bad. Definitely better than I would ever do. Then my students wanted to compare what our kicker did to the professional. I was ready for them:
We spent some time dissecting the statistics and decided that the only important value was that the professional was a 0.729 career kicker from 40-49 yards. A lot of great conversation came from whether this was a fair comparison, what stats were relevant, could we treat this as a population value, etc.
We started running the significance test, and my students led me through what should happen. They made the hypotheses, decided they needed a proportions test, figured out that a binomial distribution applies, and ran the test.
They figured out that the sample size that our kicker kicked wasn’t large enough for us to draw any usable conclusions (and I set that up on purpose). My students were so into it that they asked how large of a sample size was needed to draw valid conclusions.
I wasn’t expecting them to ask that questions, but loved that they did. They took ownership in the problem and drove the conversation themselves. All I did was guide the conversation and point out what they already knew!