A large insurance company wants to determine whether there is a difference in the average time to process claim forms among its four different processing facilities. The data in Table 10.5.1 represent weekly average number of days to process a form over a period of four weeks.
(a) Test whether there is a difference in the average processing times at the 0.05 level.
(b) Test whether there is a difference, using Tukey€™s method to find which facilities are different.
(c) Interpret your results and state any assumptions you have made in solving the problem.
Table 10.5.1

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Facility 1 1.50 0.9 1.12 1.95 Facility 2 225 1.85 1.45 2.15 Facility 3 1.30 2.75 2.15 1.55 Facility 4 2.0 2.85 5 1.15