An article by W. A. Ray et al. (Amer. J. Epidemiol. 132: 873–884, 1992) dealt with motor vehicle accident rates for 16,262 subjects aged 65–84 years, with data on each for up to 4 years. In 17.3 thousand years of observation, the women had 175 accidents in which an injury occurred. In 21.4 thousand years, men had 320 injurious accidents.

a. Find a 95% confidence interval for the true overall rate of injurious accidents.

b. Using a model, compare the rates for men and women.