Question

Question 6 (1 point)

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 7.864 minutes with a standard deviation of 2.1643 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.

Question 6 options:

1)	( 7.286 , 8.442 )

2)	( 6.142 , 9.586 )

3)	( 4.852 , 10.876 )

4)	( 6.122 , 9.606 )

5)	( -6.122 , 9.606 )

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 7.864

sample standard deviation = s = 2.1643

sample size = n = 14

Degrees of freedom = df = n - 1 = 14 - 1 = 13

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t0.005,13 = 3.012

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

= 3.012 * (2.1643 / 14)

Margin of error = E = 1.742

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

  ± E

= 7.864 ± 1.742

= ( 6.122, 9.606 )

correct option is = 4)