A scientist wishes to research the effectiveness of a flu vaccination. 150 subjects were vaccinated, 180 subjects were vaccinated with a placebo, and 100 subjects were not vaccinated. The number in each group who later caught the flu was recorded. The results are shown in the contingency table below.

Vaccinated

Placebo

Control

Caughttheflu

8

19

21

Didnotcatchtheflu

142

161

79

Use a 0.05 significance level to test the claim that the number of people who caught the flu is independent of the vaccination.

Calculate the x²test statistic to test the claim that the number of people who caught the flu is independent of the vaccination.

and

Calculate the x²critical value used to test the claim.

and

Use a 0.05 significance level to test the claim that the number of people who caught the flu is independent of the vaccination.