Real or Fake?

Yesterday I went through the PCMI probability problems from 2007 and found some really neat ideas to use over the next few weeks. I plan to use one of the activities to start us off on day 1 next week.

The basic idea is for groups to create two datasets of a coin flip. First, they will fake a dataset of 240 coin flips, then they will create a real dataset by actually flipping the coin. They will write these two datasets on index cards. Using their two datasets, they will discuss with a partner and come up with a way to determine if a new dataset is real or fake. I will then have them exchange their cards with another pair of students and use their "test" to determine which card has the real data and which card has the fake data. If time allows, there are some additional coin flip datasets in the PCMI packet that I will put up for discussion.

At some point after that - not sure if I'll do it the next day or a few weeks later - the PCMI packet went on to use an inference test to determine if a dataset was real or fake. By splitting the coinflips into sets of 2 (or 3 or whatever), you could keep track of how many HH/HT/TH/TT combinations there were and compare them to the expected 1:3:3:1 ratio. This would provide an interesting introduction to inference testing and p-values, as well as tying in to binomial expansion and pascal's triangle.

This activity should be a good way to get them back into the school frame of mind, thinking about the start of inference techniques, and drawing conclusions from data. If I'm really good this week, I'll get it together in a google form.... We'll see how that goes :)