Problem 9.14 A survey was conducted to evaluate the effectiveness of a new flu vaccine. The vaccine was provided in a two-shot sequence over a period of two weeks. Some people received the two-shot sequence, some appeared for only the first shot, and others received neither. A survey of 1000 residents the following spring provided the information shown in the table below. The researchers were interested in testing the hypothesis that the vaccine was successful in reducing the number of flu cases.

No Vaccine One Shot Two Shot Total Flu 24 9 13 46 No Flu 289 100 565 954 Total 313 109 578 1000

(a) Compute the incidence of flu for each of the three groups.

(b) Describe in plain English the null and alternative hypotheses, and which χ2 test is appropriate here: the χ2 test of independence or the χ2 test of homogeneity?

(c) Use the χ2 test described in part

(b) to test the null hypothesis, at the level α = 0.05. Describe the rejection region, decision rule, and conclusion.