Traffic engineers compared rates of traffic accidents at intersections with raised medians with rates at intersections with two-way left-turn lanes. They found that out of 4644 accidents at intersections with raised medians, 2280 were rear-end accidents, and out of 4584 accidents at two-way left-turn lanes, 1982 were rear-end accidents.

a. Assuming these to be random samples of accidents from the two types of intersection, construct a 95% confidence interval for the difference between the proportions of accidents that are of the rear-end type at the two types of intersection.

b. Does the confidence interval contradict the claim that the proportion of rear-end accidents is the same at both types of intersection?