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.

Sales Method, i	Salesman, j
	A	B	C
1	37	28	25
2	43	28	24
3	32	24	19
4	34	20	15

ANOVA: Two-Factor without Replication
SUMMARY	Count	Sum	Average	Variance
Method 1	3	90	30.0000	39.0000
Method 2	3	95	31.6667	100.3333
Method 3	3	75	25.0000	43.0000
Method 4	3	69	23.0000	97.0000
Salesman A	4	146	36.50	23.0000
Salesman B	4	100	25.00	14.6667
Salesman C	4	83	20.75	21.5833

ANOVA
Source of Variation	SS	df	MS	F	P-Value	F crit
Rows	150.2500	3	50.0833	10.93	0.0076	4.7571
Columns	531.1667	2	265.5833	57.95	0.0001	5.1433
Error	27.5000	6	4.58333
Total	708.9167	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 = 10.93, p-value = .0076; (Reject / Do not reject) : H₀: there is (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 = 57.95, p-value = .0001; (Reject / Do not reject) H₀: salesman (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) The variance F ratio seen from the table provided is 10.93. The F critical value at the 5% level is 4.7571. So we have a very strong evidence to reject H0 at alpha =0.05, and conclude that the there is a difference between the effect of the sales methods on mean weekly sales.

b) Here, the variance ratio F is given as 57.95 and the Critical value at alpha= 0.05 is 5.1433. So here also we have a very strong evidence to reject H0 and conclude that at alpha=0.05, the different salesmen have different effects on mean weekly sales.

C)