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

When the light turns yellow, should you stop or go through it? A scientific article 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 red-light runners differs between the two intersections? State the appropriate null and alternative hypotheses, use Minitab to compute the p-value of the test, then state your conclusion. Use a significance level of alpha = .05. Hand Calculation Problem: Use the confidence interval for the difference between proportions formula discussed in class and on the slides to compute a 90% confidence interval for the difference between the proportion of red-light runners at the two intersections.

Solution

a)
Null, There Is No Significance between them Ho: p1 = p2
Alternate, Proportion of red lights is diffrent b/w 2 intersection H1: p1 != p2
Test Statistic
Sample 1 : X1 =21, n1 =154, P1= X1/n1=0.136
Sample 2 : X2 =20, n2 =183, P2= X2/n2=0.109
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.122
Q^ Value For Proportion= 1-P^=0.878
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.136-0.109)/Sqrt((0.122*0.878(1/154+1/183))
Zo =0.757
| Zo | =0.757
Critical Value
The Value of |Z | at LOS 0.05% is 1.96
We got |Zo| =0.757 & | Z | =1.96
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 0.7574 ) = 0.4488
Hence Value of P0.05 < 0.4488,Here We Do not Reject Ho

We dn\'t have evidence that Proportion of red lights is diffrent b/w 2 intersection

b)
Confidence Interval for Diffrence of Proportion
CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
No. of chances( X1 )=21
No.Of Observed (n1)=154
P1= X1/n1=0.136
Proportion 2
No. of chances(X2)=20
No.Of Observed (n2)=183
P2= X2/n2=0.109
C.I = (0.136-0.109) ±Z a/2 * Sqrt( (0.136*0.864/154) + (0.109*0.891/183) )
=(0.136-0.109) ± 1.64* Sqrt(0.001)
=0.027-0.059,0.027+0.059
=[-0.032,0.086]