Mr. Cloud’s Foul Shots

We are getting dangerously close to dealing with inference in statistics. We have been working for a while on sampling distributions for means and proportions and calculating probabilities for them. I wanted to give my students an opportunity to apply their probability calculations for a purpose other than answering a question on a handout, so I gave them this:

Mr. Cloud's Free Throws Lesson_1

Any athlete in the class immediately said “no way.” I asked them to defend their argument and someone asked me to prove it. We talked and they got to the conclusion that I couldn’t prove it, but they could disprove my claim. They wanted to see me shoot some foul shots:

This confounded them a bit. I only made 45% of my free throws. They couldn’t tell whether that was different enough from 50% to say my claim was wrong. Someone finally asked for a probability to quantify their feelings:

Mr. Cloud's Free Throws Lesson_2

There’s a 32% chance that I could be a 50% free throw shooter and make 9 or less out of 20. They concluded that probablity was too high and they couldn’t disprove my claim.

Hopefully this groundwork will pay off when we officially start inference on friday.

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