1. (20 points) Suppose you observe a die-rolling game, where the player wins $3 if the...

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1. (20 points) Suppose you observe a die-rolling game, where the player wins $3 if the 6-sided die lands on a three or four and wins nothing otherwise. Based on your past observations, you suspect that the chance of a 3 or 4 with this die is less than 1/3, so you record the results of the next 61 games and observe 12 wins. (a) Can you conclude that p < 1/3? Use a significance level of 0.05. (b) What error could you have made in part (a)? 1. (20 points) Suppose you observe a die-rolling game, where the player wins $3 if the 6-sided die lands on a three or four and wins nothing otherwise. Based on your past observations, you suspect that the chance of a 3 or 4 with this die is less than 1/3, so you record the results of the next 61 games and observe 12 wins. (a) Can you conclude that p < 1/3? Use a significance level of 0.05. (b) What error could you have made in part (a)?