# Is the new vaccine better?

A vaccine for Covid-19 is known to be $$90\%$$ effective, i.e. $$90\%$$ of vaccine recipients are successfully immunised against Covid-19. A new (different) vaccine is tested on $$100$$ patients and found to successfully immunise $$96$$ of the $$100$$ patients. Is the new vaccine better?

Hint: Assume the new vaccine is equally effective as the original vaccine and consider using an appropriate distribution.

I am not sure how to tackle this problem, but my answer is:

Not necessarily, since the sample is $$100$$ and it is unknown what is the sample of the first vaccine, hence we cannot know whether the second vaccine is better.

What's the correct way to answer this problem?

• Usually, one is given a confidence level. That is, assume that the second is the same as the first and ask if the probability of the observed outcome is below the specified confidence level.
– lulu
Jul 29, 2021 at 10:38
• @lulu perhaps "the observed outcome or a more extreme outcome" Jul 29, 2021 at 10:40