Let X 1 ,,X 9 be a random sample from a N(, 1) distribution, where is

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Let X1,…,X9 be a random sample from a N(μ, 1) distribution, where μ is unknown. Suppose that we have observed the following values 16.34, 18.57, 18.22, 16.94, 15.98, 15.23, 17.22, 16.54, 17.54

We would like to decide betweenHo:  =  = 16, H:  # 16.

a. Find a 90% confidence interval around X̅. Is μ0 included in the interval? How does this relate to our hypothesis test?

b. Define a test statistic to test the hypotheses and draw a conclusion assuming α = 0.1.

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