In: Statistics and Probability
Use the information below to solve.It gives the number of city-bus users (Ridership) on a public transportation system of a large city in 3 given working days chosen at random in units of hundreds. It gives this data separately for the 4 busy bus routes and for 5 time slots. Here:
TSlot1: from start of day to 9:30 am, TSlot2: 9:30 – 12:30, TSlot3: 12:30 – 15:30, TSlot4: 15:30 – 18:30 and Time-Slot5: 18:30 to end of day
BRoute1 | BRoute2 | BRoute3 | BRoute4 |
18 | 14 | 20 | 19 |
15 | 17 | 21 | 22 |
21 | 20 | 22 | 25 |
24 | 20 | 30 | 26 |
20 | 24 | 28 | 25 |
24 | 22 | 29 | 24 |
19 | 23 | 25 | 23 |
21 | 21 | 29 | 23 |
23 | 19 | 24 | 20 |
27 | 24 | 28 | 28 |
25 | 24 | 28 | 30 |
23 | 24 | 28 | 26 |
19 | 20 | 24 | 24 |
15 | 24 | 23 | 22 |
14 | 25 | 22 | 20 |
TSlot1 | TSlot2 | TSlot3 | TSlot4 | TSlot5 |
18 | 24 | 19 | 27 | 19 |
15 | 20 | 21 | 25 | 15 |
21 | 24 | 23 | 23 | 14 |
14 | 20 | 23 | 24 | 20 |
17 | 24 | 21 | 24 | 24 |
20 | 22 | 19 | 24 | 25 |
20 | 30 | 25 | 28 | 24 |
21 | 28 | 29 | 28 | 23 |
22 | 29 | 24 | 28 | 22 |
19 | 26 | 23 | 28 | 24 |
22 | 25 | 23 | 30 | 22 |
25 | 24 | 20 | 26 | 20 |
a. Test if the mean ridership for the four bus routes are the same or different.
b. Show how the MSE can be calculated from the individual sample variances.
c. Based on the residual plots, can you comment on the aptness of this single factor model?
d. Use the Bonferroni Multiple Comparison (BMC) approach to rank (in descending order) the bus routes in terms of their mean ridership.