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	39	32	28
2	43	30	25
3	31	24	19
4	33	20	13

ANOVA: Two-Factor without Replication
SUMMARY	Count	Sum	Average	Variance
Method 1	3	99	33.0000	31.0000
Method 2	3	98	32.6667	86.3333
Method 3	3	74	24.6667	36.3333
Method 4	3	66	22.0000	103.0000
Salesman A	4	146	36.50	30.3333
Salesman B	4	106	26.50	30.3333
Salesman C	4	85	21.25	44.2500

ANOVA
Source of Variation	SS	df	MS	F	P-Value	F crit
Rows	281.5833	3	93.8611	16.98	.0025	4.7571
Columns	480.1667	2	240.0833	43.43	.0003	5.1433
Error	33.1667	6	5.52778
Total	794.9167	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 = 16.98, p-value = .0025; (Click to select)RejectDo not reject H₀: there is (Click to select)a differenceno 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 = 43.43, p-value = .0003; (Click to select)RejectDo not reject H₀: salesman (Click to select)dodo not 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)

F = 16.98, p-value = .0025; (Reject Ho): there is a difference in effects of the sales methods (treatments) on mean weekly sales.

b)

F = 43.43, p-value = .0003; (Reject H0: salesman do have an effect on sales

c)

Level of significance	0.05
no of treatments	4
df error	6
MSE	5.5278
q-statistic value	4.8956

critical value = q*√(MSE/2*(1/ni+1/nj))=6.65

confidence interval = mean difference ± critical value

if confidence interval contans zero, then means are not different.

			confidence interval
population mean difference		critical value	lower limit	upper limit	result
µ1-µ2	0.33	6.65	-6.31	6.98	means are not different
µ1-µ3	8.33	6.65	1.69	14.98	means are different
µ1-µ4	11.00	6.65	4.35	17.65	means are different
µ2-µ3	8.00	6.65	1.35	14.65	means are different
µ2-µ4	10.67	6.65	4.02	17.31	means are different
µ3-µ4	2.67	6.65	-3.98	9.31	means are not different