Perform a Chi-Square Homogeneity Test, Provided the Conditions for the Test

Essay

Perform a chi-square homogeneity test, provided the conditions for the test are met. Use the critical-value approach.
-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. Independent simple random samples were used and the number in each group who later caught the flu was recorded. The results are given in the table below, showing the test group and flu status. $$\begin{array} { r | r r r } & \text { Vaccinated } & \text { Placebo } & \text { Control } \\ \hline \text { Caught the flu } & 8 & 19 & 21 \\ \text { Did not catch the flu } & 142 & 161 & 79 \end{array}$$ Use a 5% significance level to test the claim that there is a difference in the distribution of flu status for the three test groups.