Question: Consider a random sample X1, X2, X3, X4, where each random variable X; corresponds to a coin toss that is equal to 1 with probability

Consider a random sample X1, X2, X3, X4, where each random variable X; corresponds to a coin toss that is equal to 1 with probability p and 0 with probability (1 - p). Based on a single realization 1, k2, k3, k4 of our random sample, we would like to test HO : p - 0.5 against the possibility that p > 0.5. To that effect, we choose to use the decision rule "reject HO if k = - (kj + k2 + ks + k4 ) > 1". Suppose that HO turns out to be false, and the alternative hypothesis H1: p = 0.75 turns out to be true instead. What is then the power of our decision rule? O 0.012 O 0.003 O 0.105 O 0.316
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