Swift is the holding company for Swift Transportation Co. ,Inc. ,a truckload carrier headquartered in Phoenix,Arizona.Swift operates the largest truckload fleet in the United States.Before Swift switched to its current computer-based billing system,the average payment time from customers was approximately 40 days.Suppose before purchasing the present billing system,it performed a test by examining a random sample of 24 invoices to see if the system would reduce the average billing time.The sample indicates that the average payment time is 38.7 days. The company that created the billing system indicates that the system would reduce the average billing time to less than 40 days.Conduct a hypothesis test to determine if the new computer-based billing system would reduce the average billing time to less than 40 days.Assume the standard deviation is known to be 6 days.Use a significance level of 0.025. A)Since z = -0.423 -1.96,we will not reject H₀,there is not sufficient evidence to conclude that the new computer-based billing system would reduce the average billing time to less than 40 days. B)Since z = -1.0614 -1.96,we will not reject H₀,there is not sufficient evidence to conclude that the new computer-based billing system would reduce the average billing time to less than 40 days. C)z = -1.0231 -1.96,we will reject H₀,there is sufficient evidence to conclude that the new computer-based billing system would reduce the average billing time to less than 40 days. D)z = 0.341 -1.96,we will reject H₀,there is sufficient evidence to conclude that the new computer-based billing system would reduce the average billing time to less than 40 days.

Question

Swift is the holding company for Swift Transportation Co. ,Inc. ,a truckload carrier headquartered in Phoenix,Arizona.Swift operates the largest truckload fleet in the United States.Before Swift switched to its current computer-based billing system,the average payment time from customers was approximately 40 days.Suppose before purchasing the present billing system,it performed a test by examining a random sample of 24 invoices to see if the system would reduce the average billing time.The sample indicates that the average payment time is 38.7 days. The company that created the billing system indicates that the system would reduce the average billing time to less than 40 days.Conduct a hypothesis test to determine if the new computer-based billing system would reduce the average billing time to less than 40 days.Assume the standard deviation is known to be 6 days.Use a significance level of 0.025. A)Since z = -0.423 > -1.96,we will not reject H₀,there is not sufficient evidence to conclude that the new computer-based billing system would reduce the average billing time to less than 40 days. B)Since z = -1.0614 > -1.96,we will not reject H₀,there is not sufficient evidence to conclude that the new computer-based billing system would reduce the average billing time to less than 40 days. C)z = -1.0231 > -1.96,we will reject H₀,there is sufficient evidence to conclude that the new computer-based billing system would reduce the average billing time to less than 40 days. D)z = 0.341 > -1.96,we will reject H₀,there is sufficient evidence to conclude that the new computer-based billing system would reduce the average billing time to less than 40 days.

Quizplus · Accepted Answer

We will conduct a one-tailed z-test with a significance level of 0.025.
Null hypothesis: H0: μ ≥ 40
Alternative hypothesis: HA: μ < 40 (as we are testing if the average billing time is less than 40 days)
Sample size (n) = 24
Sample mean (x̄) = 38.7
Population standard deviation (σ) = 6 (given in the problem)
z = (x̄ - μ) / (σ / √n)
z = (38.7 - 40) / (6 / √24)
z = -1.0614
As the calculated value of z is greater than the critical value of -1.96 (since we are conducting a one-tailed test), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to support the claim that the new computer-based billing system reduces the average billing time to less than 40 days.

Swift Is the Holding Company for Swift Transportation Co