A statistics professor is in a fantasy golf league with four friends. Each week one of the five people in the league is the winner of that week’s tournament. During the 2010 season, this particular professor was the winner in 7 of the first 12 weeks of the season. Does this constitute strong evidence that his probability of winning in one week was larger than would be expected if the five competitors were equally likely to win?

a. State the null hypothesis and the alternative hypothesis in the context of the study.
b. Describe how you could use playing cards to conduct a tactile simulation analysis of this study and its result. Give sufficient detail that someone else could implement this simulation analysis based on your description. Be sure to indicate how you would decide whether the observed data provide convincing evidence that the statistics professor’s probability of winning in one week was larger than would be expected if the five competitors were equally likely to win?
c. Use an applet to conduct a simulation analysis with at least 1,000 repetitions. Based on the null distribution produced by the applet, explain how you are deciding whether the observed data provide convincing evidence that the statistics professor’s probability of winning in one week was larger than would be expected if the fi ve competitors were equally likely to win. Summarize the conclusion that you would draw about the research question of whether the statistics professor’s probability of winning in one week was larger than would be expected if the five competitors were equally likely to win.
d. In answering (c), you should have reported a p-value. Interpret this p-value in the context of the study. (Hint: The p-value is the probability of what, assuming what?)
e. Explain why it is not advisable to use a one-proportion z-test (theory-based approach) to find a p-value for the data from this study.