Question: 30. Consider the hypotheses Hq:h = 10 and Hi.y. = 12, where r is the mean of a normally distributed population with variance 1. The

30. Consider the hypotheses Hq:h = 10 and Hi’.y. = 12, where r is the mean of a normally distributed population with variance 1. The prior distribution is diffuse (take a normal distribution with N' = 0), and a sample of size 10 is to be taken. If L\ = 100 and Ln = 50,

(a) find the region of rejection (using the decision-theoretic approach)

(b) from this region of rejection, find a and

(c) if Li = 50 and Ln = 50, what would the region of rejection be?

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