The serum cholesterol levels for 20-24 year old males in the US has mean 180 mg/100ml and standard deviation σ = 46 mg/100ml. We are interested in the mean cholesterol level of the larger population of 20-74 old males, say µ. Suppose, we have a random sample of size 25 from the larger population. We want to test the following hypotheses at significance level α = 0.01: H0 : µ = 180, HA : µ > 180
a) What is the probability of Type I error?
b) Suppose the true value of µ = 211. Then what is the power of this test? What is the probability of making a Type II error?
c) If α is fixed at 0.01, how will you increase the power of the test?
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