Question

You must download the file “Assn3_Qu#2_W19” to use the required data. 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 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.

BRoute1   BRoute2   BRoute3   BRoute4
27 24   28   28
25   24   28   30
23   24   28   26
19   20   24   24
15   24   23   22
14   25   22   20
19   23   25   23
21   21   29   23
23   19   24   20
24   20   30   26
20   24   28   25
24   22   29   24
18   14   20   19
15   17   21   22
21   20   22   25

Answer 1

a. Test if the mean ridership for the four bus routes are the same or different.

Ans:

Source	DF	SS	MS	F	P
Route	3	272.8	90.9	7.52	0.000
Error	56	677.3	12.1
Total	59	950.2

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.

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?

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.

Multiple Comparisons
Y Bonferroni
(I) Time	(J) Time	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
					Lower Bound	Upper Bound
BRoute1	BRoute2	-1.5333	1.26992	1.000	-5.0068	1.9402
	BRoute3	-5.5333*	1.26992	.000	-9.0068	-2.0598
	BRoute4	-3.9333*	1.26992	.018	-7.4068	-.4598
BRoute2	BRoute1	1.5333	1.26992	1.000	-1.9402	5.0068
	BRoute3	-4.0000*	1.26992	.016	-7.4735	-.5265
	BRoute4	-2.4000	1.26992	.384	-5.8735	1.0735
BRoute3	BRoute1	5.5333*	1.26992	.000	2.0598	9.0068
	BRoute2	4.0000*	1.26992	.016	.5265	7.4735
	BRoute4	1.6000	1.26992	1.000	-1.8735	5.0735
BRoute4	BRoute1	3.9333*	1.26992	.018	.4598	7.4068
	BRoute2	2.4000	1.26992	.384	-1.0735	5.8735
	BRoute3	-1.6000	1.26992	1.000	-5.0735	1.8735

a