Question

You must download the file "Assn3Ou#2W19" to use the required data. Ît 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, TSlotl: 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 Test if the mean ridership for the four bus routes are the same or different. Show how the MSE can be calculated from the individual sample variances. Based on the residual plots, can you comment on the aptness of this single factor model? Use the Bonferroni Multiple Comparison (BMC) approach to rank (in descending order) the bus routes in terms of their mean ridership. a. b. c. d. TSlot2 TSlot3 TSlot4 TSlot5 18 TSlot1 19 15 14 20 24 25 24 23 27 BRoute1 BRoute2BRoute3 BRoute3 14 24 20 24 20 24 25 23 24 24 24 28 28 28 28 30 26 20 19 18 15 23 23 25 26 25 24 23 23 20 20 20 24 30 28 29 25 29 24 28 28 28 24 24 20 24 19 17 20 20 25 29 30 23 21 19 24 24 24 20 24 25 29 26 25 24 24 23 23 20 19 23 27 25 23 19 15 14 20 30 26 24 25 23 20

Answer 1

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, Time-Slot 1: from start of day to 9:30 am, Time-Slot 2:9:30 - 12:30, Time-Slot 3: 12:30 15:30, Time-Slot 4: 15:30 18:30 and Time-Slot 5: 18:30 to end of day. a. Test if the mean ridership for the four bus routes are the same or different. Ans: MS F Source DF Route 3 Error 56 677.3 121 Total9950.2 2728 90.97.520.000 Comment: The p-value of Route is 0.000 and less than 0.05. Hence, the mean ridership for the four bus routes is different at 0.05 level of significance that is at least one route has the significant mean difference.

C. Based on the residual plots, can you comment on the aptness of this single factor model? Residual Plots for Y_1 Normal Probability Plot Versus Fits 0.1 -10 10 20 24 26 Residual Fitted Value Histogram Versus Order 10.0 7.5 S.0 2.5 0.0 6 4 -20 26 Residual 15 10 15 20 25 30 35 40 45 50 55 60 Observation Order From the above residual plots, we can conclude that the assumptions of the normality, randomness, and homoscedasticity are satisfied. Hence, it is appropriateness 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. Multlple Comparlson:s Bonferroni 9596 Confidence Interval Mean iffeence Std. Lower Upper (I) Time (J) Time Error Sig Bound Bound 15333 1.26992 10005.0068 19402 BRoute35.5333 1269920009.006820598 BRoute43.9333 126992 .0187.40684598 1.5333 1.26992 10001.9402 5.0068 (I-J) BRoutel BRoute2 BRoute2 BRoute1 BRoute34000 126992 .016747355265 BRoute424000 1.26992384 -5.87351.0735 BRoute3 BRoutei5.5333 126992.000 205989.0068 BRoute2 4.0000 126992 .016.526574735 BRoute4 1.6000 1.26992 1.000-187355.0735 BRoute4 BRoutel 3.9333 126992 018 4598 7.4068 BRoute2 | 24000 | 1.26992 | 384 | -1.0735 | 5.8735 1.6000 | 1.26992 | 1.000 | -50735 | 1.8735 BRoute3