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 653.5 vehicles per hour, with a standard deviation of 311.7 vehicles per hour. A traffic engineer states that the mean improvement is between 581 and 726 vehicles per hour. With what level of confidence can this statement be made? Express the answer as a percent and round to the nearest integer.The level of confidence is what % ?

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joaobezerra joaobezerra · Answer 1 · 2019-11-08T19:00:23+01:00

Answer:

The confidence level is 90%.

Step-by-step explanation:

To find the confidence level, we have to find how many degrees of freedom there are and what is the value of T.

Our sample size is 50.

This means the number of degrees of freedom is 50 subtracted by 1, that is [tex]df = 49[/tex].

The standard deviation of our sample is

[tex]s = \frac{\sigma}{\sqrt{50}} = \frac{311.7}{\sqrt{50}} = 44.08[/tex].

The lower end of the confidence interval is:

[tex]L = \mu - T*s[/tex]

The mean is 653.5, so [tex]\mu = 653.5[/tex], The lower end of the interval is 581. So

[tex]L = \mu - T*s[/tex]

[tex]581 = 653.5 - 44.08T[/tex]

[tex]44.08T = 72.5[/tex]

[tex]T = 1.645[/tex]

Now, we already have T. So looking at the t-table, with [tex]df = 49, T = 1.645[/tex], we have that the confidence level is 90%.