Two Proportions - Practice Problem 2

Are seat belts effective?

A simple random sample of front-seat occupants involved in car crashes is obtained. Among 2823 occupants not wearing seat belts, 31 were killed. Among 7765 occupants wearing seat belts, 16 were dead (based on data from "Who Wants Airbags?" by Meyer and Finney, Chance, Vol. 18. No. 2). Therefore, we want to use a 0.05 significance level to test that seat belts effectively reduce fatalities.

a: Test the claim using hypothesis test.

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

c: What does the result suggest about the effectiveness of seat belts?