Answer: Absolutely yes.
Explanation:
It's vital we investigate to know of the new method is even much better as far as percentage of success is concerned.
SAMPLE SIZE : 80
SUCCESSFUL DETECTION = 80-9= 71
PERCENTAGE OF FAILURE = 100 - % OF SUCCESS. or
THE PERCENTAGE OF FAILURE = (9/80) × 100% = 11.25 %
It is clear that this new method definitely detects cancer much better than the previous one and consequently for that sample size is sufficiently large to hypothesize if the new method detects cancer better.