Question: X1, ... X16 are a random sample from a N(, 5 2 ) population. To test the hypotheses H0: = 100 vs. H1: = 102,

X1, ... X16 are a random sample from a N(, 5 2 ) population. To test the hypotheses H0: = 100 vs. H1: = 102, a statistician uses the test: Reject H0 if X > c, where c is a real number.

i) Find the value of c for which this test will have a significance level of 0.025.

Hint: If X1, ... X16~ i. i. d. N(, 5 2 ), then what is the distribution of X? In particular, what is its distribution under H0?

ii) Determine the power of the test for the value of c found in part (i)

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