A standard drug is known to be effective in 80% of the cases in which it is used. A new drug is tested on 100 patients and found to be effective in 85 cases. Is the new drug superior? (Hint: Evaluate the probability of observing 85 or more successes assuming that the new and old drugs are equally effective.)
For the solution I used the Binomial Equation, but I'm not sure if it is correct?
P(x greater than or equal to 85) = 1 - P(X less than equal to 84) = 1 - Summation from x=84 to 100 ((100 choose x) (0.8^x) (0.2^(100-x)) = 0.129
But I'm not sure about the interpretation. This is telling me that there is a 12.9% probability that 85 new cases would be observed given a success rate of .8. But how would I conclude from this if the new drug is superior or not? And is this solution even correct?