1) [7 pts.] In the magical realm ruled by King Arthur, there has recently been an alarming increase in the number of knights and princesses eaten by fire-breathing dragons. There is, of course, concern that this high-fat diet will result in increased levels of heart disease among the kingdom's dragons. To counter this growing health risk, Merlin the Magician has developed special diet pills for dragons. He swears that dragons that eat the pills immediately before a meal will subsequently eat fewer knights and princesses. Because you are the most respected professor of numerology at the University of Camelot in South Devonshire (UCSD), King Arthur hires you to test Merlin's claim. You randomly select 9 fire-breathing dragons, and the number of knights and princesses eaten by each dragon is measured twice: once when the dragon has eaten Merlin's pills prior to a meal ("WITH PILLS"), and once when the dragon has not eaten these pills prior to a meal ("NO PILLS"). (Assume that appropriate counter-balancing is employed, and that all necessary assumptions for the appropriate hypothesis test have been met.)