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.

Question

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.

Quizplus · Accepted Answer

The Answer is

\mathrm { H } _ { 0 }

: The proportion of people catching the flu is the same in all three groups.

\mathrm { H } _ { 1 }

: The proportions are different.
Test statistic:

\chi ^ { 2 } = 14.965

. Critical value:

\chi ^ { 2 } = 5.991

.
Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the proportion of people catching the flu is the same in all three groups.

A Researcher Wishes to Test the Effectiveness of a Flu