Refer to Exercises 10.54 and 10.55. To obtain a more accurate picture of the impact of air bags on preventing deaths, it is necessary to account for the effect of occupants using both seat belts and air bags. If the occupants of the vehicles in which air bags are installed are more likely to be also wearing seat belts, then it is possible that some of the apparent effectiveness of the air bags is in fact due to the increased usage of seat belts. Thus, one more 2 × 2 table is necessary: the table displaying a comparison of proper seat belt usage for occupants with air bags available and for occupants without air bags available. Those data are given here.

a. Is there significant evidence of an association between air bag installation and the proper usage of seat belts? Use a = .05
b. Provide justification for your results in part (a).

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Seat Belt Usage Air Bags Yes No Total Seat Belt 4.871.940 2,902,694 7774.634 No Seat Belt 870,875 1,952211 2,823086 Total 5,742.815 4,854905 10597720