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I need help with the exercise below:

To investigate the effect of a new vaccine, 150 out of 300 sick animals were given the vaccine and the remaining 150 were given nothing. After a while, 10 of those who were given the vaccine and 30 who were not given the vaccine died. In this case, assuming $\alpha=0.05$ can we say that the vaccine decreases the proportion of death? In addition what would the power of the test be?

I stated the hypothesis as follows:

$H_0: P_{vaccine}=P_{No-vaccine}$

$H_1: P_{vaccine} < P_{No-vaccine} $

What formula should I use for the test statistics?

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  • $\begingroup$ What would justify your assumption that the vaccine could not possibly do any harm? $\endgroup$
    – whuber ♦
    Commented Jan 6, 2015 at 12:58
  • $\begingroup$ I am not sure what you mean.Can you be more clear? $\endgroup$
    – Günal
    Commented Jan 6, 2015 at 13:00
  • $\begingroup$ Consider your alternative hypothesis: what does it say? $\endgroup$
    – whuber ♦
    Commented Jan 6, 2015 at 13:09
  • $\begingroup$ It says the vaccine decreases the proportion of death, doesn't it? $\endgroup$
    – Günal
    Commented Jan 6, 2015 at 13:10
  • $\begingroup$ In other words, H0 and H1 are supposed to be exhaustive and mutually exclusive. In the current form, the possibility that $P_{v+} > P_{v-}$ is not accounted for. $\endgroup$
    – Penguin_Knight
    Commented Jan 6, 2015 at 15:37

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