1) I keep struggling with the concept of a "Null Hypothesis". In particular, the situation of testing to see if a coin is biased. My best shot at a hypothesis and null hypothesis for this is situation is:
Case 1-- believe the die is unfair Hypothesis: The results I have recorded are caused by the die being loaded (biased or unfair). Null Hypothesis: The results I have recorded show no significant affect of the die being loaded. Case 2-- believe the die is fair Hypothesis: The results I have recorded are caused by the die being fair (unbiased). Null Hypothesis: The results I have recored show no significant affect of the die being fair.
2) Chi-squared-- other than making sure the values are positive, why square?
My kids are really are tearing it up with TinkerPlots. It is really neat to see them be able to mess about with different approaches to decide what they believe to be the answer to problem. They had to decide if a die I gave them was loaded or not, and collecting the data while making a live histogram really helped them get a feel for how many trials they would need to feel "80% convinced" they had it right. They had a strong suspicion at 10, were pretty convinced by 20, and were at least 80% convinced by 30 trials. When the answer was revealed, and they saw they were right, they were pretty happy.