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 JMP output of a randomized block ANOVA of these data.

	Salesman, j
Sales Method, i	A	B	C
1	32	29	30
2	32	30	28
3	27	25	23
4	25	24	23

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Ratio
Model	5	116.66667	23.3333	35.0000
Error	6	4.00000	0.6667	Prob > F
C. Total	11	120.66667	24.0000	0.0002*

Effect Tests
Source	Nparm	DF	Sum of Squares	F Ratio	Prob > F
Method	3	3	98.000000	49.0000	0.0001*
Salesman	2	2	18.666667	14.0000	0.0055*

Least Squares Means Estimates
Method	Estimate	Salesman	Estimate
1	30.333333	A	29.000000
2	30.000000	B	27.000000
3	25.000000	C	26.000000
4	24.000000

Tukey HSD All Pairwise Comparisons

Quantile = 3.46171, Adjusted DF = 60, Adjustment = Tukey

Method -Method		Difference	Std Error	t Ratio	Prob>|t|	Lower 95%	Upper 95%
1	2	0.333333	0.6666667	0.50	0.9561	−1.97447	2.641140
1	3	5.333333	0.6666667	8.00	0.0008*	3.02553	7.641140
1	4	6.333333	0.6666667	9.50	0.0003*	4.02553	8.641140
2	3	5.000000	0.6666667	7.50	0.0012*	2.69220	7.307800
2	4	6.000000	0.6666667	9.00	0.0004*	3.69220	8.307800
3	4	1.000000	0.6666667	1.50	0.4919	−1.30780	3.307800

(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?

(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?

(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 3 decimal places. Negative amounts should be indicated by a minus sign.)

Answer 1