A manufacturer frequently sends small packages to a customer in another city via air freig...

A manufacturer frequently sends small packages to a customer in another city via air freight, and, in many cases, it is important for a package to reach the customer as soon as possible. Three different firms offer air freight service, including pickup and delivery, on a 24-hour basis. The head of the manufacturer’s shipping department would like to know whether the firms differ in speed of service and whether the time of day makes any difference. An experiment is designed to investigate these issues. Packages are sent at random times, and the air freight firm used for each package is also randomly chosen. The customer records the time that each package arrives, so that the time elapsed during shipment can be determined. These limes are rounded to the nearest hour. The experimental results for a total of 54 packages are shown in the following table.

a. What evidence is relevant for deciding whether the choice of best firm will be different at different times of the day? What conclusion can you draw using a 5% level of significance? Construct a graph that depicts the nature of any differences in firm as a function of the time of day.

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b. Does any firm appear to be better than the other two firms? How could you compare the best firm and the second-best firm using a confidence interval?