Let X1,., X,n be a simple random sample from a normal distribution with unknown mean u and variance o? = 1. Suppose n = 8 and we want to perform a test of Η : μ 0 HA : µ>0 vs. with significance level a = 0.05. A. We learned a sign test for a median M. Suppose we perform a sign test for the mean u by relying on the fact that, because a normal distribution is symmetric, its mean and median are the same, so a test for the mean is equivalent to a test for the median. Under the null hypothesis, what is the probability that X; is greater than 0? 0.5 B. Suppose we are performing a sign test for the mean/median. Under the null hypothesis, what is the probability that there are at least seven X;'s are greater than 0? 0.03516 C. Find the power of the sign test supposing mean u = 0.5. 0.40 True D. True or False: the power of the sign test depends on the population variance.

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A: The solution is given below in the next step:

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A: Given that: 57-24

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A: