Amie Jackson, a manager at Sigma travel services, makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process. The travel website is open for reservations 24 hours a day, and Amie regularly checks the website for the waiting time to maintain consistency in service. She uses the following independently drawn samples of wait time during two peak hours, morning 8 a.m. to 10 a.m. and evening 7 p.m. to 9 p.m., for the analysis. Assume that wait times are normally distributed. Which of the following is the correct value of the test statistic?
A) 1.72
B) 2.96
C) 1.66
D) 0.34

Question

Amie Jackson, a manager at Sigma travel services, makes every effort to ensure that customers attempting to make online reservations do not have to wait too long to complete the reservation process. The travel website is open for reservations 24 hours a day, and Amie regularly checks the website for the waiting time to maintain consistency in service. She uses the following independently drawn samples of wait time during two peak hours, morning 8 a.m. to 10 a.m. and evening 7 p.m. to 9 p.m., for the analysis. Assume that wait times are normally distributed.  Which of the following is the correct value of the test statistic?
A) 1.72 
B) 2.96 
C) 1.66 
D) 0.34

Quizplus · Accepted Answer

Since the sample size is greater than 30 for both morning and evening peak hours, we can use the z-test. We are given that wait times are normally distributed, so we can use the formula:
z = (x̄ - μ) / (σ / √n)
where x̄ is the sample mean, μ is the population mean (which we don't know), σ is the population standard deviation (which we don't know), and n is the sample size.

For morning peak hours:
x̄ = 4.2 minutes
σ = 1.8 minutes
n = 50
We want to test whether the population mean wait time is greater than 4 minutes. So our hypotheses are:
H0: μ ≤ 4
Ha: μ > 4 (right-tailed test)

The test statistic is:
z = (4.2 - 4) / (1.8 / √50) = 1.72

For evening peak hours:
x̄ = 4.7 minutes
σ = 1.7 minutes
n = 60
We want to test whether the population mean wait time is greater than 5 minutes. So our hypotheses are:
H0: μ ≤ 5
Ha: μ > 5 (right-tailed test)

The test statistic is:
z = (4.7 - 5) / (1.7 / √60) = -2.96

Therefore, the correct value of the test statistic is 2.96 for evening peak hours.

Amie Jackson, a Manager at Sigma Travel Services, Makes Every