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A Researcher Wishes to Test the Effectiveness of a Flu

Question 21

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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.  Vaccinated  Placebo  Control  Caught the flu 81921 Did not catch the flu 14216179\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.

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