The primary problem of Session 8 is based on the question, "After several practices of Push Penny, have you developed skill in playing the game?"
This is a statistics problem; appropriate data consist of the results from several rounds of the game. The ultimate goal of this session is to compare the experimental results with the expected results, using a probability model.
First, you play 20 games and record the results from each game. Next, you consider whether the results indicate that you are a skillful Push Penny player. You then analyze the results for a person who played 100 games of Push Penny. Finally, based on these data, you try to determine whether the player did in fact develop any Push Penny skills.
Make sure that you allow time to develop your own ideas for analysis. In considering whether skill has been demonstrated, you may want to look at the average score or at the proportion of hits from all 400 pushes.
Both the average score and the proportion of hits depend on basic probability concepts. In order to determine whether the proportion of hits demonstrates skill, you must first consider the probability that a random push will hit a line. The "average" score depends on a concept of average other than the arithmetic mean: In this case, it is a weighted mean where the weights are probabilities.
The method of analysis investigated in this session -- "goodness of fit" -- uses the binomial probability model. At this point, it is important to consider how probability can be used in the analysis of this problem. You will return to the problem of determining skill after considering some basic ideas about probability.
<< back to Part A: Probability in Statistics