Testing Hypothesis (vaccine)

[Agent Smith]

TL;DR Summary

Vaccine efficacy hypothesis using a method that may/may not be appropriate

Placebo/control group has 800 people. They aren't given the vaccine. 60 of them develop the disease
Treatment group has 1000 people. They're given the vaccine. 15 develop the disease

It seems there's a formula viz $\frac{p_1 - p_2}{\sqrt{p (1 - p)}\left(\frac{1}{n_1} + \frac {1}{n_2}\right)}$ to do this.

However I tried something different. Would like to know if it's valid.

For $p_1$ = proportion of diseased in unvaccinated and $p_2$ = proportion of diseased in vaccinated, my hypotheses are:
$H_0: p_2 =p_1$
$H_a: p_2 < p_1$

Is this ok?

 

[Dale]

It is equivalent. Your $H_0$ can be tested by seeing if the above formula is significantly different from 0.