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 at all. The number in each
group who later caught the flu was recoreded. The results are shown below.
Vaccinated Placebo Not Vacc.control
Obs. Freq. who caught the flu 8 19 21
obs freq who DIDNOT catch 142 161 79
Exp freq who CAUGHT flu ? ? ?
Exp freq who DIDNOT catch ? ? ?
A) Calculate the expected frequency for people to catch and not to catch the flu if the probability of
catching the flu is the same in all three groups.
Expected frequency Caught
Vaccinated
Vaccinated with
placebo
Not vaccinated
Expected frequency
not Caught
150*((8+19+21)/(150+180+100))=16.74 150-16.74=133.26
20.09
159.91
11.16
88.84
B) Use the 0.05 significance level to test the claim that the proportion of people catching the flu is the
same in all three groups.
Use chi-square test
(8-16.74)2/16.74+(19-20.09)2/20.09+(21-11.06)2/11.06=13.55>5.991=20.05(2)
Then we can conclude that proportion of people catching flu is not same in these three
groups.