In a fair Pick 3 game, the first digit drawn should be a zero with probability...

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In a fair "Pick 3" game, the first digit drawn should be a zero with probability 0.1 because there are ten equally likely outcomes. A lottery player suspects that the game is unfair. To test his theory, he records the numbers drawn over two years which constitute 582 plays. a) (4 points) Write down the critical region for testing whether or not the probability of drawing a 0 first is actually 1/10. Use a level of a = 0.05. b) (7 points) If he finds that 48 out of 582 times the first number was zero, what does the test conclude? Use both RR and p-value to reach the conclusion. c) (4 points) What is the B of this test versus the alternative hypothesis that p= 0.075? In a fair "Pick 3" game, the first digit drawn should be a zero with probability 0.1 because there are ten equally likely outcomes. A lottery player suspects that the game is unfair. To test his theory, he records the numbers drawn over two years which constitute 582 plays. a) (4 points) Write down the critical region for testing whether or not the probability of drawing a 0 first is actually 1/10. Use a level of a = 0.05. b) (7 points) If he finds that 48 out of 582 times the first number was zero, what does the test conclude? Use both RR and p-value to reach the conclusion. c) (4 points) What is the B of this test versus the alternative hypothesis that p= 0.075?

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