The business office of a large university is in the process of selecting amongst the Postal Service and three private couriers as its sole delivery method for the university's responses to applications for admission. After consulting with the university's statistics department, it was decided that over the next month the following study would be conducted. Ten cities with at least 100 applicants would be selected for inclusion in the study. To each of these cities 100 standard packages would be sent by each of the four methods of delivery. The percentage of packages not delivered within five days was recorded for each method of delivery yielding the following data. For four of the cities, at least one of the methods of delivery did not provide service and hence there are missing data in these cells.
|
City
|
|
Method
|
C1
|
C2
|
C3
|
C4
|
C5
|
C6
|
C7
|
C8
|
C9
|
C10
|
|
M1
|
*
|
90.2
|
82.9
|
89.4
|
98.0
|
91.5
|
97.2
|
83.4
|
88.6
|
*
|
|
M2
|
87.1
|
99.5
|
92.0
|
91.4
|
99.2
|
91.5
|
97.6
|
88.7
|
92.7
|
97.6
|
|
M3
|
91.6
|
99.7
|
*
|
99.2
|
99.3
|
98.1
|
98.2
|
95.4
|
93.7
|
98.3
|
|
M4
|
95.5
|
99.9
|
93.8
|
98.9
|
99.4
|
98.6
|
*
|
94.1
|
93.1
|
99.3
|
a. Obtain the sum of squares for an AOV table by fitting complete and reduced models using a statistical software program.
b. Is there significant evidence of a difference in the four methods of delivery based on the percentage of packages delivered within five days?