A Researcher Wishes to Test the Effectiveness of a Flu

Essay

A researcher wishes to test the effectiveness of a flu vaccination. 150 people are vaccinated, 180 people are vaccinated with a placebo, and 100 people are not vaccinated. The number in each group who later caught the flu was recorded. The results are shown below.
$$\begin{array} { r | r r r } & \text { Vaccinated } & \text { Placebo } & \text { Control } \\\hline \text { Caught the flu } & 8 & 19 & 21 \\\text { Did not catch the flu } & 142 & 161 & 79\end{array}$$
Use a 0.05 significance level to test the claim that the proportion of people catching the flu is the same in all three groups.