5. (8 points) A basketball player shoots 50 free throws in a local gym. He successfully makes 45 of his free throws.
a. Test the hypothesis (using an approximate test) that this player has a higher free throw percentage than 85%. Use O = 0.02.
b. Report the p-value in (a).
6. (8 points) There are two decks of cards. Each deck has cards of two colors which are red and black, and the number of cards in each deck is unknown as well as the number of cards in each deck that are red. Let P1 be the proportion of cards in deck 1 that are red, and P2 be the proportion of cards in deck 2 that are red. Suppose we draw 100 cards from deck 1 with replacement and 144 cards from deck 2 with replacement. 67 cards drawn from deck 1 show red, and 99 cards from deck 2 show red.
a. Test the hypothesis (using an approximate test) that the proportion of red cards in decks 1 and 2 are different. Use O = 0.02.
b. Report the p-value in (a).
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