2) The drug Prevnar is a vaccine meant to prevent certain types of bacterial meningitis. It is typically administered to infants starting around 2 months of age. In randomized, double-blind clinical trials of Prevnar, infants were randomly divided into two groups. Subjects in Group 1 received Prevnar, while subjects in Group 2 received a control vaccine. After the second dose, 137 of 452 subjects in the experimental group (Group 1) experienced drowsiness as a side effect. After the second dose, 31 of 99 subjects in the control group (Group 2) experienced drowsiness as a side effect. a) Test the claim that a different proportion of subjects in Group 1 experienced drowsiness as a side effect than subjects in Group 2 at the a= 0.05 level of significance. b) Construct a 99% confidence interval for the difference between the two population proportions. c) Does your confidence interval agree with your hypothesis test? Explain how