By law, all new cars must be equipped with both driver-side and passenger side safety air bags. There is concern, however, over whether air bags pose a danger for children sitting on the Passenger side. In a National Highway Traffic Safety Administration (NHTSA) study of 55 people killed by the explosive force of air bags, 35 were children seated on the front-passenger side. (Wall Street Journal, January 22, 1997.) This study led some car owners with children to disconnect the passenger-side air bag. Consider all fatal automobile accidents in which it is determined that air bags were the cause of death. Let p represent the true proportion of these accidents involving children seated on the front-passenger side.
a. Use the data from the NHTSA study to estimate p.
b. Construct a 99% confidence interval for p.
c. Interpret the interval, part b, in the words of the problem.
d. NHTSA investigators determined that 24 of 35 children killed by the air bags were not wearing seat belts or were improperly restrained. How does this information impact your assessment of the risk of an air bag fatality?