MATH SOLVE

3 months ago

Q:
# 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. At the intersection of Route 7 and North Shrewsbury in Clarendon, Vermont, 154 vehicles were observed to encounter a yellow light in the indecision zone, and 21 of them ran the red light. At the intersection of Route 62 and Paine Turnpike in Berlin, Vermont, 183 vehicles entered the intersection in the indecision zone, and 20 ran the red light. Can you conclude that the proportion of redlight runners differs between the two intersections?

Accepted Solution

A:

Answer:No, does not differ.Step-by-step explanation:Given that there are two intersections route 7 and route 62.At the intersection of Route 7 and North Shrewsbury in Clarendon, Vermont, 154 vehicles were observed to encounter a yellow light in the indecision zone, and 21 of them ran the red light. At the intersection of Route 62 and Paine Turnpike in Berlin, Vermont, 183 vehicles entered the intersection in the indecision zone, and 20 ran the red light.Let p1 be the first proportion and p2 the secondWe want to test whether these two proportions differ[tex]H_0: p_1 = p_2\\H_a: p_1 \neq p_2[/tex](two tailed test at 5% significance level)test statistic = [tex]\frac{p_1-p_2}{\bar p (1-\bar p)(\frac{1}{n_1}+\frac{1}{n_2})}[/tex][tex]p_1 = 0.1363\\p_2 = 0.1093[/tex]Z statistic = [tex]0.7554[/tex]p value = 0.4473Since p >0.05 accept null hypothesis.There is no significant difference and the proportion of redlight runners does not differ between the two intersections