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When the light turns yellow, should you stop or go through

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 11E Chapter 5.2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 11E

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.

Step-by-Step Solution:

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).

Step 3 of 4

Chapter 5.2, Problem 11E is Solved
Step 4 of 4

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The full step-by-step solution to problem: 11E from chapter: 5.2 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. The answer to “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.” is broken down into a number of easy to follow steps, and 165 words. Since the solution to 11E from 5.2 chapter was answered, more than 353 students have viewed the full step-by-step answer. This full solution covers the following key subjects: light, yellow, zone, indecision, vehicles. This expansive textbook survival guide covers 153 chapters, and 2440 solutions.

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