Question

The article"Modeling Arterial Signal Optimization with Enhanced Cell Transmission Formulations" (Z. Li, Journal of Transportation Engineering2011:445–454) presents a new method for timing traffic signals in heavily traveled intersections. The effectiveness of the new method was evaluated in a simulation study. In 50 simulations, the mean improvement in traffic flow in a particular intersection was 654.1 vehicles per hour, with a standard deviation of 311.7 vehicles per hour.

Activities:

1. Find a 95% confidence interval for the improvement in traffic flow due to the new system.

Answer 1

To find a 95% confidence interval for the improvement in traffic flow due to the new system, use the mean and standard deviation of the improvements. Apply the formula: Confidence Interval = Mean Improvement ± (Critical Value × Standard Deviation / √Sample Size). Finally, calculate the upper and lower bounds.

Step-by-step explanation:

To find a 95% confidence interval for the improvement in traffic flow due to the new system, we can use the formula:

Confidence Interval = Mean Improvement ± (Critical Value × Standard Deviation / √Sample Size)

Given that the mean improvement is 654.1 vehicles per hour and the standard deviation is 311.7 vehicles per hour, we need to determine the critical value based on a 95% confidence level. The critical value for a 95% confidence level is 1.96.

Plugging in the values into the formula, we get:

Confidence Interval = 654.1 ± (1.96 × 311.7 / √50)

Simplifying the expression, we find:

Confidence Interval = 654.1 ± 87.88

Therefore, the 95% confidence interval for the improvement in traffic flow due to the new system is (566.22, 741.98) vehicles per hour.