Let X1, X2, . . . , Xn iid∼ N (µ, σ2 ). Consider the hypotheses...

Let X1, X2, . . . , Xn iid∼ N (µ, σ2 ).

Consider the hypotheses H0 : µ = µ0 and H1 : µ (not equal)= µ0 and the test statistic (X bar − µ0)/ (S/√ n). Note that S has been used as σ is unknown.

a. What is the distribution of the test statistic when H0 is true?

b. What is the type I error of an α−level test of this type? Prove it.

c. What is the type II error of an α−level test of this type? Prove it.

d. Describe the properties of the type II error function for this test.

e. How can a 100(1 − α)% confidence interval be used to carry out this test? Prove it.

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Expert Solution

orchestra answered 1 year ago

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