Refer to Exercise 14.

a. Find a \(95 \%\) upper confidence bound for the mean improvement.

b. Find a \(98 \%\) lower confidence bound for the mean improvement.

Data From Exercise 14:

The article "Modeling Arterial Signal Optimization with Enhanced Cell Transmission Formulations" (Z. Li, Journal of Transportation Engineering, 2011:445-454) 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.