Question

Suppose you are a civil engineer, specializing in traffic volume control for the City of Birmingham. 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 8 cars, the average wait time is 6.126 minutes with a standard deviation of 2.1681 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.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 6.126 minutes

sample standard deviation = s = 2.1681 minutes

sample size = n = 8

Degrees of freedom = df = n - 1 = 8 - 1 = 7

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t_0.005,7 = 3.499

Margin of error = E = t_/2,df * (s /n)

= 3.499 * ( 2.1681/ 8)

Margin of error = E = 2.682

The 99% confidence interval estimate of the population mean is,

  ± E

= 6.126  ± 2.682

=( 3.444, 8.808 ) minutes.