Question

A regional bank manager wants to know the difference between the mean amounts of time customers wait in line at the drive-up window for three banks in his region. He randomly sampled seven wait times from each location. The data are given in the tables below.

	Bank 1	Bank 2	Bank 3
1	1.81	3.34	2.32
2	1.43	1.77	1.23
3	1.92	2.80	1.89
4	2.45	1.72	2.31
5	1.99	1.84	3.00
6	1.80	2.38	1.93
7	1.32	1.96	2.45

Groups	Count	Sum	Average	Variance	Std Dev
Bank 1	7	12.72	1.817143	0.139724	0.373796
Bank 2	7	15.81	2.258571	0.378414	0.615154
Bank 3	7	15.13	2.161429	0.304748	0.552040

Source of Variation	SS	df	MS	F
Between Groups	SSTr	dfTr	MSTr	1.373095
Within Groups	SSE	18	MSE
Total	5.690581	20

(a)

What is the sum of squares treatment? (Round your answer to five decimal places.)

(b)

What is the sum of squares error? (Round your answer to five decimal places.)

(c)

What is the mean squares treatment and the mean squares error? (Round your answers to four decimal places.)

MSTr=MSE=

Answer 1

	Bank 1	Bank 2	Bank 3
	1.81	3.34	2.32
	1.43	1.77	1.23
	1.92	2.8	1.89
	2.45	1.72	2.31
	1.99	1.84	3
	1.8	2.38	1.93
	1.32	1.96	2.45
Total(yi)	12.72	15.81	15.13
Averages y̅i	1.817143	2.258571	2.161429
Treatment Effect	1.8171 - 2.079 = -0.2619	2.2586 - 2.079 = 0.1796	2.1614 - 2.079 = 0.0824

Overall total = 43.66
Overall mean µ = 43.66 / 21 = 2.07905

y̅i .. is overall mean
y̅i. is treatment mean
SST = ΣΣ(Yij - & Y̅..)²
SS treatment = ΣΣ(Yij - & y̅i.)²
SS error = Σ(y̅i. - & Y̅..)²

	Sum of Squares	Degree of freedom	Mean Square	F0 = MST / MSE	P value
Treatment	0.75327	2	0.37664	1.37315	0.2786
Error	4.93728	18	0.27429
Total	5.69055	20

Part a)

SS treatment = ΣΣ(Yij - & y̅i.)² = 0.75327

Part b)

SS error = Σ(y̅i. - & Y̅..)² =  4.93728

Part c)

MS treatment = SS treatment / a-1 = 0.3766

MS error = SS error / N - a = 0.2743