The Decrease in Cholesterol Level After Eating a Certain Brand

Multiple Choice

The decrease in cholesterol level after eating a certain brand of oatmeal for breakfast for one month in people with cholesterol levels more than 200 mg/dl is Normally distributed, with mean (in milligrams) μ and standard deviation σ= 3. The brand advertises that eating its oatmeal for breakfast daily for one month will produce a mean decrease in cholesterol of more than 10 points for people with cholesterol levels more than 200 mg/dl, but you believe that the mean decrease in cholesterol is actually less than advertised. To explore this question, you test the following hypotheses at the 0.05 level:
H₀: μ= 10, H_a: μ< 10
You carry out the level 0.05 test by randomly selecting 100 people with cholesterol levels more than 200 mg/dl and, after they have eaten this brand of oatmeal for one month, computing the mean decrease x̄ in the subjects' cholesterol levels. What is the probability of a Type II error for your test at μ= 8.5?

A) 0.0004
B) 0.0012
C) 0.9988
D) 0.9996