# Day 103: Share the Rainbow

The activity we did today in AP Stats was an Introduction to the Logic of Hypothesis Testing using Skittles.  I wrote this activity after being inspired by Adam Pethan’s video Hypothesis Tests: Introduction.  He had a wonderfully simple way of using a real life scenario (that used food) and gave me an awesome activity that connected sampling distributions to this new idea.

Because I wanted (needed) the sample size to be controlled and the sample proportion to be the same for all students, I used Adam’s random sample proportion of yellow skittles as the basis for building the logic of the hypothesis test.  They needed to draw the population distribution (labeled correctly) and write both hypotheses correctly with correct symbols (this is the FIRST time they have ever seen a Null or Alternative hypothesis).  They had to show me their answers on these first questions before they could get Skittles.  It gave me a chance to check every single hypothesis along with symbols and notation…great formative assessment.

Once the student wrote the two hypotheses correctly along with the hypothesized population distribution, they could get a mini-cup of Skittles to munch on while they continued with the activity.

During our study of sampling distributions, I emphasized ad nauseam what the probability meant and had the kids write an interpretation of the probability they calculated in their own words based on the mean of the sampling distribution AND the sample statistic comparison.  In particular, the focus was on the idea of the sample being “unusual” in our sampling distribution as reflected by the probability we calculated dovetailed easily into today’s lesson.  They determined what their level of tolerance for an unusual sample value would be based on the probability (area).  This will lead in nicely to alpha levels later in the unit.

Then they calculated the probability using the sample value and the constructed sampling distribution (of course they checked the conditions to build the distribution!!)  But looking over their submissions, we still have to work on testing the Normal condition…but we have months to do this, right?  Formative assessment is so great for highlighting misconceptions and missing details, isn’t it?  I also gave a silent yelp of joy as my students talked, discussed, argued, clarified and focused on understanding the big ideas.

The last part of the activity reviewed confidence intervals again since the kiddos are having their test tomorrow on this topic.  Very few questions to me, but lots of intense discussion about how/why to approach these questions.  I would say that the 7 of the 8 math practices were in evidence today: sense-making, reasoning, argument, modeling, using tools, precision of language and calculations, and attending to the inherent structure of the problem.

Finally, they submit their results electronically in Schoology so I can look at the results and determine the next steps.  All in all, I was really pleased with the success of this first-time activity.  I did work out the problems ahead of time, but using with students is always eye-opening.  Some tweaking is needed, but not as much as some of my first-time activities need.  How do you vet  your activities (make a careful and critical examination of them) before you use them for the first time?