Cheater? A group of curious college students decide to test the integrity of their fellow collegians. In order to see if students will cheat, when given an opportunity, they decide to use chocolately M&M's. They tell each student that a discerning palette will be able to tell the difference in flavor between and red and a yellow candy. The blindfolded subjects are given two piles of candy to test. But the experimenter turns his back so that the subject thinks that they have a window of opportunity to take a quick peak. Unbeknownst to the subjects, there is another helper who is hidden and secretly watching to see who cheats. Here is their data.
a. What is the probability that a subject cheated?
b. If a subject was a male, what are the chances that they cheated?
c. Using your answers to (a) and (b), does it appear that cheating and gender are independent?
d. A statistics student in the group decides she wants to run a Chi-square test for independence. Why would this not be an advisable choice?
e. An argument begins. The girls are suggesting that the guys cheated more than girls; and that this difference is larger than can be explained by chance variation. Of course, the guys insist that with a small sample size like this, anything could happen. Fortunately, a randomization machine is discovered. The 18 observations are randomly placed into the 4 categories randomly. This procedure is repeated 1000 times and the number of male cheaters is counted each time. A graph is below. What does this graph tell you about the claims of the two groups?
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