Question

A new method for timing traffic signals in heavily traveled intersections is introduced. 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. Approximately what sample size is needed so that a 98% confidence interval will specify the mean to within ± 50 vehicles per hour?

Answer 1

Answer:

The sample size must be approximately 211.

Step-by-step explanation:

We are given the following in the question:

Sample mean, $\bar{x}$ =  654.1

Alpha, α = 0.02

Population standard deviation, σ = 311.7

Margin of error  = 50

Formula:

$z_{critical}\frac{\sigma}{\sqrt{n}}$

$z_{critical}\text{ at}~\alpha_{0.02} = \pm 2.33$

Putting all the values, we get,

$\pm 50 = \pm 2.33 (\dfrac{311.7}{\sqrt{n}} ) \\\\\sqrt{n} = \dfrac{2.33\times 311.7}{50}\\\\n = 210.98\\n \approx 211$

Thus, the sample size must be approximately 211.