I am Jerry Reiter, a 3rd year graduate student in statistics at Harvard University. I am very interested in the teaching of statistics and in how the AP statistics exam is taking shape. I am looking forward to learning about teaching statistics by participating in this group!
A great example for demonstrating hypothesis testing for p-hat is the following:
Take 20 pennies (20 is arbitrary, just make it a relatively large number) and stand them up on their edges on a table. Bang the table with a moderate amount of force. How many pennies do you expect will land heads up?
It turns out that the tails side of a penny is heavier, so heads comes up a lot more than 50% of the time! I haven't done it with a large number of pennies, but I usually get 80% heads or more!
This is a fun example to test againt the null p=0.5. If you have lots of students doing the example, you will likely find some accepting the null hypothesis. This will show the variability inherent in hypothesis testing.