Question

When the light turns yellow, should you stop or go through it? An 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 20 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? Find the P-value and state a conclusion. Round the answer to four decimal places.

Answer 1

Probability: 0.7190

There is not enough evidence at the 5% level of significance to suggest that there is difference in proportions of red-light runners between the two intersections

Explanation:

We can conduct a hypothesis test for the difference of 2 proportions. If there is no difference in proportion of red-light runners between the 2 lights, then the difference in proportions will be zero. That makes the null hypothesis

H0: p1 - p2 = 0

The question is asking whether there is a difference, meaning that the difference can be higher or lower. If there is a difference, the proportions are not equal. This makes the alternate hypothesis

Ha: p1 - p2 ≠ 0

This is a two tailed test

We will use a significance level of 95% to conduct our test. This makes the critical values for our test statistic: z > 1.96 or z < -1.96.

If our test statistic falls in either region, we will reject the null hypothesis.

See the attached photo for the hypothesis and conclusion

The z-value of the test statistic is z = 0.58.

P(z < 0.58) = 0.7190