Final answer:
The observed rate of headaches among Lipitor users in the clinical trial (47 out of 863) is significantly lower than the expected rate if 10% truly experienced headaches, given the very low probability of such an observation. This would indeed support the claim that fewer than 10% of subjects treated with Lipitor experience headaches.
Step-by-step explanation:
The question revolves around the efficacy of atorvastatin (brand name Lipitor), a drug in the class of medications known as statins, which are used to lower cholesterol levels. In a clinical trial, 47 out of 863 subjects experienced headaches, which is a result that must be evaluated to determine if it is significantly low given the claim that fewer than 10% of subjects treated with Lipitor experience headaches.
If the true rate of headaches in subjects taking Lipitor was 10%, and the observed rate in the study (47 out of 863) yielded a probability of 0.000000987 of observing 47 or fewer headaches, this result is significantly lower than what would be expected by chance alone. Hence, this would support the claim that fewer than 10% of subjects treated with Lipitor experience headaches. In statistical terms, since the probability is much less than the conventional significance level (alpha) of 0.05, we would reject the null hypothesis that the true rate is 10% or higher, thus supporting the claim.