Question 1111073: The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) \mu and standard deviation \sigma = 0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5, but you believe that the mean nicotine content is actually higher than advertised. To explore this, you test the hypotheses H_0: \mu = 1.5, H_a: \mu > 1.5 and you obtain a P-value of 0.052. Which of the following is true?
A. At the \alpha = 0.05 significance level, you have proven that H_0 is true.
B. This should be viewed as a pilot study and the data suggests that further investigation of the hypotheses will not be fruitful at the \alpha = 0.05 significance level.
C. There is some evidence against H_0, and a study using a larger sample size may be worthwhile.
D. You have failed to obtain any evidence for H_a.
*I am pretty sure the answer to this question is C, but I just wanted a second opinion in case I am actually wrong. Thank you so much!*
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! C is reasonable. One can make the case that one either rejects or fails to reject Ho. But a p-value so close to the significance level suggests that increasing the sample size with the same difference would show significance.
A and B clearly are not correct.
One can make a case for D, but most would say there is evidence, even if Ho was not rejected.
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