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"A group of test subjects are split into two groups. 1000 people are given a vaccine, and 15 of them get the disease. 800 people are given a placebo, and 60 of them get the disease. Test the hypothesis that the vaccine is effective at $\alpha = 0.05$."

I know that I am supposed to be testing $H_0: \mu_1 = \mu_2$ vs. $H_1: \mu_1 < \mu_2$. I think, but need clarification, that the formula I need for the test is

$$z = \frac{p_1 - p_2}{\sqrt{p(1-p)\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}}$$

where

$$p = \frac{x_1 + x_2}{n_1 + n_2}$$

Is this correct? If so, I just plug in $p_1 = \frac{15}{1000}$, $p_2 = \frac{60}{800}$, $n_1 = 800$, $n_2 = 1000$, and $p = \frac{15 + 60}{800 + 1000}$, then compare $z$ to $z_{0.05}$. Correct?

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    $\begingroup$ Please add the self-study tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. $\endgroup$
    – kjetil b halvorsen ♦
    Commented Feb 25 at 19:56
  • $\begingroup$ @kjetil b halvorsen, I tried using the formulas listed above. What I need is clarification that I am on the right track or if I need to try something else. $\endgroup$
    – Forklift17
    Commented Feb 25 at 20:01

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