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	35	28	24
2	42	32	25
3	32	24	20
4	32	20	15

ANOVA: Two-Factor without Replication
SUMMARY	Count	Sum	Average	Variance
Method 1	3	87	29.0000	31.0000
Method 2	3	99	33.0000	73.0000
Method 3	3	76	25.3333	37.3333
Method 4	3	67	22.3333	76.3333
Salesman A	4	141	35.25	22.2500
Salesman B	4	104	26.00	26.6667
Salesman C	4	84	21.00	20.6667

ANOVA
Source of Variation	SS	df	MS	F	P-Value	F crit
Treatments (Sales Methods)	191.5833	3	63.8611	22.32	.0012	4.7571
Blocks (Salesmen)	418.1667	2	209.0833	73.08	.0001	5.1433
Error	17.1667	6	2.86111
Total	626.9167	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 = 22.32, p-value = .0012; (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 = 73.08, p-value = .0001; (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) 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 = 22.32, p-value = .0012;

Reject H₀: there is no difference in effects of the sales methods (treatments) on mean weekly sales.

Because p<0.05.

(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 = 73.08, p-value = .0001;

Reject H₀: Salesman do not have an effect on sales.

Because p<0.05.

(C)

We know that

then,