Problem 4. (4 points) A game studio is producing a competitive video game with three char- acter classes, supposedly balanced so that no particular class is more powerful than the rest. (a) In 100 independent matches, the following numbers of victories per class are observed: n1 = 32, r12 = 29, ns = 39. How well does the data support the hypothesis that the game is balanced as intended? Give the p-value. (b) The game studio is acquired by an unscrupulous publisher and introduces a fourth, pre- mium class that needs to be purchased separately and is designed to win 1.2x more often than non-premium classes. In 200 independent matches, the following numbers of victories per class are observed: n1 = 42, n2 = 47, n3 = 39, n4 = 72. How well does the data support the hypothesis that the game is balanced as intended (three equally powerful classes and the 1.2x advantage for class 4)? Give the p-value