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.

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