A study investigated rates of fatalities among patients with serious traumatic injuries. Among 61,909 patients transported by helicopter, 7813 died. Among 161,566 patients transported by ground services, 17,775 died (based on data from "Association Between Helicopter vs Ground Emergency Medical Services and Survival for Adults With Major Trauma," by Galvagno et al., Journal of the American Medical Association, Vol. 307, No. 15). Use a 0.01 significance level to test the claim that the rate of fatalities is higher for patients transported by helicopter.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

c. Considering the test results and the actual sample rates, is one mode of transportation better than the other? Are there other important factors to consider?