Let X 1 ,,X 9 be a random sample from a N(, 1) distribution, where 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 between a Find a 90 confidence interval around X Is 0 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 0 1 Ho 16, H 16

Question: Let X 1 ,,X 9 be a random sample from a N(, 1) distribution, where is unknown. Suppose that we have observed the following

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 between Ho: = = 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.

Ho: = = 16, H: # 16.

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