Question

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?

Please show work

Answer 1

Ans:

a)Probability of type I error=alpha=0.01

b)

sample mean cut off value=180+2.326*(46/sqrt(25))=201.399

z=(201.399-211)/(46/sqrt(25))

z=-1.044

Power=P(z>-1.044)=0.8517

Probability of type II error=1-0.8517=0.1483

c)We can increase the sample size to increase the power.

Larger the n,larger the test statistic,lower the p-value,we will be more likely to reject the null hypothesis,hence increased power.