When the light turns yellow, should you stop or go through it? The article “Evaluation of Driver Behavior in Type II Dilemma Zones at High-Speed Signalized Intersections” (D. Hurwitz, M. Knodler, and B. Nyquist, Journal of Transportation Engineering 2011:277–286) defines the “indecision zone” as the period when a vehicle is between 2.5 and 5.5 seconds away from an intersection. It presents observations of 710 vehicles passing through various intersections in Vermont for which the light turned yellow in the indecision zone. Of the 710 vehicles, 89 ran a red light.

a. Find a 90% confidence interval for the proportion of vehicles that will run the red light when encountering a yellow light in the indecision zone.

b. Find a 95% confidence interval for the proportion of vehicles that will run the red light when encountering a yellow light in the indecision zone.

c. Find a 99% confidence interval for the proportion of vehicles that will run the red light when encountering a yellow light in the indecision zone.

Answer:

Step 1 of 4:

Given, the indecision zone as the period when a vehicle is between 2.5 and 5.5 seconds away from an intersection. It presents observations of 710 vehicles passing through various intersections in Vermont for which the light turned yellow in the indecision zone. Of the 710 vehicles, 89 ran a red light.

Here,

x = 89, n = 710

Step 2 of 4:

a). To find a 90% confidence interval for the proportion of vehicles that will run the red light when encountering a yellow light in the indecision zone.

Then,

= 710+ 4

= 714.

=

A 90% confidence interval for ‘p’ is given by

For a 90% confidence interval:

Z - value for 90% confidence interval is

Then,

=

=

(0.1069, 0.1479)

Therefore, a 90% confidence interval for the proportion of vehicles that will run the red light when encountering a yellow light in the indecision zone is (0.1069, 0.1479).