Question

An airline has four ticket counter positions at a particular airport. The airline has set a new goal of limiting the waiting times for its customers at the counters to not more than 5 minutes. As part of its effort to reduce the waiting time, the airline has introduced the ‘snake system’. Under this system, all customers enter a single waiting line that winds back and forth in front of the counter. A customer who reaches the front of the line proceeds to the first free position. Each weekday for six weeks, the airline customer-relations manager charts the waiting time in minutes for the first customer entering after 4:00 PM. The resulting data show a sample mean waiting time of 4.1 minutes with estimated population standard deviation of 1.1 minutes. Using the given information please calculate and interpret the 90% confidence interval for the mean waiting time of customers of the airline. Please show the necessary steps. Based on your results, is it reasonable to conclude that the airline is achieving its stated goal? Please justify your answer.    ​

Answer 1

n= 5 days * 6weeks = 30 days

mean waiting time= 4.1 minutes

population standard deviation =1.1 minutes

M = 4.1
Z critical value = 1.64
sM = √(1.1^2/30) = 0.2

μ = M ± Z(sM)
μ = 4.1 ± 1.64*0.2
μ = 4.1 ± 0.33

90% CI [3.77, 4.43].

You can be 90% confident that the population mean (μ) falls between 3.77 minutes and 4.43 minutes

Since the 90% confidence interval does NOT contain null hypothesis value therefore it is significant. Hence it is reasonable to conclude that the airline is achieving its stated goal.