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 obtain a P-value of 0.052. Which of the following is TRUE?

A) At the α= 0.05 significance level, you have proved that H₀ is true.
B) You have failed to obtain any evidence for H_a.
C) There is some evidence against H₀, and a study using a larger sample size may be worthwhile.
D) This should be viewed as a pilot study, and the data suggest that further investigation of the hypotheses will not be fruitful at the α= 0.05 significance level.