A large retail company has to deliver its goods to distributors throughout the country. It has been offered trial-run services by three transportation companies. To test the efficiency of these three companies, it randomly assigns its outgoing product shipments to these transporters and determines the degree of lateness as a proportion of the time allocated for delivery. Table 12-38 shows the degree of lateness of the three companies for five shipments,
(a) Is there a difference in the mean degree of lateness of the three transportation companies? Test at the 10% level of significance.
(b) Find a 95% confidence interval for the mean degree of lateness of company 1.
(c) Find a 90% confidence interval for the difference in the mean degree of lateness of companies 2 and 3. Can we conclude that there is a difference in their means at the 10% level of significance?
(d) Which company would you choose? Why?

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Transportation Company 0.04 0.15 0.06 0.00 0.11 0.03 Degree of Lateness Values 0.02 0.07 0.04 0.03 0.09 0.04 0.02 0.12 0.05