Question

An article 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 652.6 vehicles per hour, with a standard deviation of 311.7 vehicles per hour. Find a 98% confidence interval for the improvement in traffic flow due to the new system. Round the answers to three decimal places. The 98% confidence interval is

Answer 1

Answer:

The 98% confidence interval is (546.586 ,758.614).

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 50

Sample mean = 652.6 vehicles per hour

Sample standard deviation = 311.7 vehicles per hour

98% confidence interval:

$\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}$  

Putting the values, we get,  

$t_{critical}\text{ at degree of freedom 49 and}~\alpha_{0.02} = \pm 2.405$  

$652.6 \pm 2.405(\dfrac{311.7}{\sqrt{50}} ) =652.6 \pm 106.014 = (546.586 ,758.614)$  

The 98% confidence interval is (546.586 ,758.614).