The serum cholesterol levels for 20-24 year old males in the US has mean mu = 18

Question

The serum cholesterol levels for 20-24 year old males in the US has mean mu = 180 mg/100ml and standard deviation sigma = 46 mg/100ml. We are interested in the mean cholesterol level of the larger population of 20-74 old males. Suppose, we have a random sample of size 25 from the larger population. We want to test the following hypotheses at significance level alpha = 0.01: H_0 : mu = 180, H_A : mu > 180 a) What is the probability of making a Type I error? b) Suppose the true value of mu = 211. Then what is the power of this test? What is the probability of making a Type II error? c) If alpha is fixed at 0.01, how could you increase the power of the test?

Explanation / Answer

a)

Z=(211-180)/46/sqrt(100)=6.7

P is:0

So probability of making type I error is:0

b)

power of test is:99%

Type II Error = 1- power = 1-0.99 = 0.01

c)

we can not increase power of test

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