Answer the question

(b) A researcher wishes to test the effectiveness of a flu vaccination. Out of a total of 430 people, 150 are vaccinated, 180 are vaccinated with a placebo, and 100 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 8 19 21 Did not catch the flu 142 161 79 Use a 5% significance level to test the claim that the proportion of people catching the flu is the same in all three groups. [Note: the test statistic value is 14.965] (6 marks)