Question

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 14 cars, the average wait time is 6.313 minutes with a standard deviation of 1.6509 minutes. Construct a 90% confidence interval for the true average wait time for a car at the intersection between 4:00 PM and 5:00 PM. 1) (4.542, 8.084).2) (5.536, 7.09). 3) (-5.532, 7.094).4) (5.532, 7.094).5) (5.872, 6.754).

Answer 1

90% Confidence Interval = (5.532, 7.094)

Explanation:

With a sample size of 14 cars, the average wait time is 6.313 minutes with a standard deviation of 1.6509 minutes. Construct a 90% confidence interval for the true average wait time for a car at the intersection between 4:00 PM and 5:00 PM. 1) (4.542, 8.084).2) (5.536, 7.09). 3) (-5.532, 7.094).4) (5.532, 7.094).5) (5.872, 6.754).

We are given the sample size = 14 cars

This sample size is small so instead of using z score , we would use the t score critical value

First we need to calculate our degree of freedom

Degrees of freedom = n - 1

= 14 - 1 = 13

The t score for 90% confidence interval with a degree of freedom of 13 =

= 1.771

Hence, Confidence Interval =

Mean ± t score × standard deviation/√n

= 6.313 ± 1.771 × 1.6509/√14

= 6.313 ± 1.771 × 0.4412215843

= 6.313 ± 0.7814034257

Confidence Interval

= 6.313 - 0.7814034257

= 5.5315965743

≈ 5.532

= 6.313 + 0.7814034257

= 7.0944034257

≈ 7.094

90% Confidence Interval = (5.532, 7.094)