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	28	23
2	39	28	25
3	31	24	20
4	35	21	14

ANOVA: Two-Factor without Replication
SUMMARY	Count	Sum	Average	Variance
Method 1	3	90	30.0000	67.0000
Method 2	3	92	30.6667	54.3333
Method 3	3	75	25.0000	31.0000
Method 4	3	70	23.3333	114.3333
Salesman A	4	144	36.00	14.6667
Salesman B	4	101	25.25	11.5833
Salesman C	4	82	20.50	23.0000

ANOVA
Source of Variation	SS	df	MS	F	P-Value	F crit
Rows	118.9167	3	39.6389	8.25	.0150	4.7571
Columns	504.5000	2	252.2500	52.49	.0002	5.1433
Error	28.8333	6	4.80556
Total	652.2500	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 = 8.25, p-value = .0150;   (Click to select)   Do not reject   Reject   H₀: there is   (Click to select)   a difference   no 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 = 52.49, p-value = .0002;   (Click to select)   Do not reject   Reject   H₀: salesman   (Click to select)   do   do 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 = 8.25, p-value = .0150; Reject H0: there is    a difference    in effects of the sales methods (treatments) on mean weekly sales.

b)

Reject   H0: salesman    do    have an effect on sales

c)

Level of significance	0.05
no. of treatments,k	4
DF error =N-k=	6
MSE =	4.8056
q-statistic value(α,k,N-k)	4.8956

critical value = q*√(MSE/2*(1/ni+1/nj))
confidence interval = mean difference ± critical value

			confidence interval
population mean difference	critical value	lower limit	upper limit
µ1-µ2	-0.67	6.19608	-6.86	5.53
µ1-µ3	5.00	6.20	-1.20	11.20
µ1-µ4	6.67	6.20	0.47	12.86
µ2-µ3	5.67	6.20	-0.53	11.86
µ2-µ4	7.33	6.20	1.14	13.53
µ3-µ4	1.67	6.20	-4.53	7.86

sales method(s) 2 maximize mean weekly sales