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Suppose you are a civil engineer, specializing in traffic volume control for the City of Grand Rapids. Your department has been receiving a multitude of complaints about traffic wait times for a certain intersection in the heart of downtown. To see if these claims are valid, you want to monitor the true average wait time at that intersection. Over the course of a few months, you record the average number of minutes a car waits at the intersection between 4:00 PM and 5:00 PM. With a sample size of 9 cars, the average wait time is 6.79 minutes with a standard deviation of 2.2175 minutes. Construct a 99% confidence interval for the true average wait time for a car at the intersection between 4:00 PM and 5:00 PM.

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Answer:

(4.31 ; 9.27)

Step-by-step explanation:

Given :

Sample size , n = 9

Mean, x = 6.79

Standard deviation = 2.2175

The confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * s/√n

Zcritical at 99% ; df = n - 1 = 9 - 1 = 8 = 2

Zcritical at 99% = 3.355

Margin of Error = 3.355 * 2.2175/√9 = 2.480

Lower boundary = 6.79 - 2.480 = 4.31

Upper boundary = 6.79 + 2.480 = 9.27

(4.31 ; 9.27)

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