Suppose the mean cholesterol level of 20 children whose fathers died from heart disease is 190 mg/dl and the sample standard deviation is 50 mg/dl. You hypothesize that the true population mean is 175 mg/dl, which is the cholesterol level of children whose fathers did not die from heart disease. Since it is believed that the cholesterol level cannot be lower than this, a one-sided test is used at the 0.01 significance level.
a. What is the probability of making a type II error?
b. How would the sample size change if we are only will to risk a 5% chance failing to reject a false null hypothesis?
c. How large of a sample size would be needed if we are only willing to risk a 10% chance of failing to reject a false null hypothesis?
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