Mr. Crow, the principal at Arizona State University agreed to participate in a dunking booth during the homecoming fair. Here's how the booth worked:
People who purchased tickets would push a button. The button operated a light above the booth, and the light was programmed to flash either green or red using a randomizing mechanism. If the light turned green, Mr, Crow was dunked, but if it turned red he stayed dry. He was told the light was set to have a 50% chance of turning green.
As it turned out, Mr. Crow seemed to be getting dunked more than 50% o f the time. In fact, over 20 pushes of the button, he had been dunked 15 times! He was pretty suspicious of what he had gotten himself into.
questions:
3.) Suppose the fair continued and Mr. Crow was dunked 46 times out of 60 pushes on the button. Would that convince you that the dunking booth was not set the way he had been told? What about 72 dunks out of 100 pushes?
4.) Mr. Crow's experience - 15 dunks out of 20 pushes of the button - represented 75% dunks. Question 3 asked about other examples involving approximately 75% dunks. If you were not convinced by either result in question 3 that the booth was not set to 50% green, how many occurrences of about 75% dunks would it take to convince you of that? IF you were convinced by the results described in question 3, what is the smallest 75% dunk result that would convince you? In either case, explain your answer.