Question: Consider the coin-tossing experiment mentioned in class where there are two coins, Coin 0 and Coin 1, with probability p of heads equal to 0.7

Consider the coin-tossing experiment mentioned in class where there are two coins, Coin 0 and Coin 1, with probability p of heads equal to 0.7 and 0.5, respectively. Professor Rajaratnam is handed one of the coins (he does not know which one), which he tosses until a heads comes up. The total number of tosses X is recorded, and based on this, we form a hypothesis test of the following hypotheses: H0 : p = 0.7 H1 : p = 0.5 (a) What is the significance level of a test that rejects H0 if X 3? Hint: If X has a geometric distribution, then P (X x) = 1 (1 p)x. (b) What is the power of the test described in part (a)

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