11.19 Severity of fever after flu shot The study mentioned in Example 5 also looked at the severity of fever (rated as mild, moderate or severe) for all subjects who developed one after receiving a flu shot. The following table shows counts for subjects randomized to the group that received the active ingredient of the flu shot and the placebo group that received a sugar injection.

a. Researchers want to know whether the distribution of the severity of fever is the same in both groups.
Formulate appropriate null and alternative hypotheses.

b. The X2 value for these data equals 2.49. Based on the df for the chi-squared distribution, argue that this value is not extreme.

c. The P-value for the chi-squared test equals 0.287.
Write the conclusion of the test in context.

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Severity Group Mild Moderate Severe Active 39 12 12 Placebo 19 11 4