Traffic engineers compared rates of traffic collisions at intersections with raised medians and rates at intersections with two-way left-turn lanes. They found that out of 4,512 collisions at intersections With raised medians, 2,202 were rear-end collisions, and out of 4,277 collisions at two-way left-turn Lanes, 1,903 were rear-end collisions.
Assuming these to be random samples of collisions from the two types of intersections, construct a 95% Confidence interval for the difference between the proportions of collisions that are of the rear-end Type at the two types of intersection. Does the confidence interval contradict the claim that the Proportion of rear-end collisions is the same at both types of intersection?

Question

Quizplus · Accepted Answer

Let p1 denote the proportion of rear-end collisions at intersections with raised medians and p2 denote the proportion of rear-end collisions at intersections with two-way left-turn lanes.

The point estimate for the difference between the proportions is:

p1 - p2 = (2202/4512) - (1903/4277) = 0.078

To construct the confidence interval, we can use the formula:

(p1 - p2) ± z*√[(p1*(1-p1)/n1) + (p2*(1-p2)/n2)]

where z* is the critical value from the standard normal distribution for a 95% confidence level, which is 1.96.

Plugging in the values, we get:

0.078 ± 1.96*√[(0.078*(1-0.078)/4512) + (0.044*(1-0.044)/4277)]

Simplifying, we get:

0.078 ± 0.016

So the 95% confidence interval is (0.062, 0.094).

Since this interval does not contain zero, we can conclude that the difference between the proportions of rear-end collisions is statistically significant at the 5% level. Therefore, we reject the claim that the proportion of rear-end collisions is the same at both types of intersection.

Traffic Engineers Compared Rates of Traffic Collisions at Intersections with Raised