Question

The article "Modeling Arterial Signal Optimization with Enhanced Cell Transmission Formulations" (Z Li. Journal ofTransportation Engineering 2011:445"454) presents a new method for timing traffic signals in heavily traveledintersections. The effectiveness of the new method was evaluated in a simulation study. In 50 simulations. the meanimprovement in traffic flow in a particular intersection was 654.1 vehicles per hour, with a standard deviation of 311.7vehicles per hour. Find a 95% confidence interval for the improvement in traffic flow due to the new system.

Answer 1

Using a sample mean of 654.1 and a standard deviation of 311.7 for 50 simulations, the 95% confidence interval for the improvement in traffic flow is (567.66, 740.54) vehicles per hour.

Step-by-step explanation:

The 95% confidence interval for the improvement in traffic flow using the new system can be calculated using the formula for a confidence interval of the mean, which is the sample mean ± the margin of error. The margin of error is found by multiplying the standard deviation by the z-score corresponding to the desired level of confidence, and then dividing by the square root of the sample size. Given the mean improvement of 654.1 vehicles per hour, a standard deviation of 311.7 vehicles per hour, and a sample size of 50, we first calculate the margin of error.

Thus, the margin of error is 1.96 × 311.7 / √50, which equals approximately 86.44. The confidence interval is therefore 654.1 ± 86.44, which results in a lower bound of 567.66 and an upper bound of 740.54 vehicles per hour. The 95% confidence interval for the mean improvement in traffic flow is (567.66, 740.54) vehicles per hour.