Question

A marketing organization wishes to study the effects of four sales methods on weekly sales of a product. The organization employs a randomized block design in which three salesman use each sales method. The results obtained are given in the following table, along with the Excel output of a randomized block ANOVA of these data.

	Salesman, j
Sales Method, i	A	B	C
1	36	32	25
2	41	31	26
3	33	23	19
4	35	20	13

ANOVA: Two-Factor without Replication
SUMMARY	Count	Sum	Average	Variance
Method 1	3	93	31.0000	31.0000
Method 2	3	98	32.6667	58.3333
Method 3	3	75	25.0000	52.0000
Method 4	3	68	22.6667	126.3333
Salesman A	4	145	36.25	11.5833
Salesman B	4	106	26.50	35.0000
Salesman C	4	83	20.75	36.2500

ANOVA
Source of Variation	SS	df	MS	F	P-Value	F crit
Rows	204.3333	3	68.1111	9.25	.0114	4.7571
Columns	491.1667	2	245.5833	33.36	.0006	5.1433
Error	44.1667	6	7.36111
Total	739.6667	11

(a) Test the null hypothesis H₀ that no differences exist between the effects of the sales methods (treatments) on mean weekly sales. Set α = .05. Can we conclude that the different sales methods have different effects on mean weekly sales?

F = 9.25, p-value = .0114; (Click to select)RejectDo not reject H₀: there is (Click to select)no differencea difference in effects of the sales methods (treatments) on mean weekly sales.

(b) Test the null hypothesis H₀ that no differences exist between the effects of the salesmen (blocks) on mean weekly sales. Set α = .05. Can we conclude that the different salesmen have different effects on mean weekly sales?

F = 33.36, p-value = .0006; (Click to select)Do not rejectReject H₀: salesman (Click to select)do notdo have an effect on sales

(c) Use Tukey simultaneous 95 percent confidence intervals to make pairwise comparisons of the sales method effects on mean weekly sales. Which sales method(s) maximize mean weekly sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Method 1 – Method 2:	[, ]
Method 1 – Method 3:	[, ]
Method 1 – Method 4:	[, ]
Method 2 – Method 3:	[, ]
Method 2 – Method 4:	[, ]
Method 3 – Method 4:	[, ]

Answer 1

a) p-value = 0.0114 which is less than alpha 0.05 hence we reject null hypothesis and conclude that there is a significant difference in effects of the sales methods (treatments) on mean weekly sales.

b) p-value = 0.0006 which is less than alpha 0.05, hence we reject null hypothesis and conclude that salesman do have an effect on sales.

c)

Tukey Simultaneous Tests for Differences of Means

Difference of Method Levels	Difference of Means	SE of Difference	Simultaneous 95% CI	T-Value	Adjusted P-Value
1 - 2	-1.67	2.22	(-9.34, 6.01 )	0.75	0.873
1 -3	6.00	2.22	(-1.68 , 13.68, )	-2.71	0.122
1 - 4	8.33	2.22	(0.66 , 16.01, )	-3.76	0.036
2 - 3	7.67	2.22	(-0.01 , 15.34, )	-3.46	0.050
2 - 4	10.00	2.22	(2.32 , 17.68,)	-4.51	0.016
3 - 4	2.33	2.22	(- 5.34 , 10.01)	-1.05	0.727

Method 2 maximize mean weekly sales because it is significantly different from method 4 and higher interval values for sales.