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
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. |
Click here for the Excel Data File |
Salesman,j | |||
Sales Method,i | A | B | C |
1 | 40 | 28 | 26 |
2 | 40 | 31 | 23 |
3 | 33 | 22 | 15 |
4 | 35 | 19 | 15 |
ANOVA: Two-Factor without Replication | ||||
SUMMARY | Count | Sum | Average | Variance |
Method 1 | 3 | 94 | 31.3333 | 57.3333 |
Method 2 | 3 | 94 | 31.3333 | 72.3333 |
Method 3 | 3 | 70 | 23.3333 | 82.3333 |
Method 4 | 3 | 69 | 23.0000 | 112.0000 |
Salesman A | 4 | 148 | 37.00 | 12.6667 |
Salesman B | 4 | 100 | 25.00 | 30.0000 |
Salesman C | 4 | 79 | 19.75 | 31.5833 |
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-Value | F crit |
Rows | 200.2500 | 3 | 66.7500 | 17.80 | .0022 | 4.7571 |
Columns | 625.5000 | 2 | 312.7500 | 83.40 | .0000 | 5.1433 |
Error | 22.5000 | 6 | 3.75000 | |||
Total | 848.2500 | 11 | ||||
(a) | Test the null hypothesisH0that no differences exist between the effects of the sales methods (treatments) on mean weekly sales. Set = .05. Can we conclude that the different sales methods have different effects on mean weekly sales? |
F = 17.80,p-value = .0022;(Click to select)Do not rejectRejectH0: there is(Click to select)no differencea differencein effects of the sales methods (treatments) on mean weekly sales. |
(b) | Test the null hypothesisH0that no differences exist between the effects of the salesmen (blocks) on mean weekly sales. Set = .05. Can we conclude that the different salesmen have different effects on mean weekly sales? |
F = 83.40,p-value = .0000;(Click to select)RejectDo not rejectH0: salesman(Click to select)dodo nothave 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: | [,] |
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