Exercise 12.15 (Algo) METHODS AND APPLICATIONS 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 34 29 30 2 32 30 28 3 28 25 23 4 25 24 23 Analysis of Variance Sum of Mean Source DF Squares Square F Ratio Model 5 136.4166? 27.2833 25.1846 Error 6 6.50000 1.0833 Prob > F C. Total 11 142.9166? 28.3666 0.0006* Effect Tests Sum of Source Nparm DF Squares F Ratio Prob > F Method 3 3 106.250000 32.6923 0.0004* Salesman 2 2 30.166670 13.9231 0.0056* Least Squares Means Estimates Method Estimate Salesman Estimate 1 31.000000 A 29.750000 2 30.000000 B 27.000000 3 25.333333 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 1.000000 0.8498366 1.18 0.6613 -1.94188 3.941880 1 3 5.666667 0.8498366 6.67 0.0023* 2.72478 8.608550 1 4 7.000000 0.8498366 8.24 0.0007* 4.05812 9.941880 2 3 4.666667 0.8498366 5.49 0.0061* 1.72478 7.608550 2 4 6.000000 0.8498366 7.06 0.0017* 3.05812 8.941880 3 4 1.333333 0.8498366 1.57 0.4586 1.60855 4.275220 (a) Test the null hypothesis H0 that no differences exist between the effects of the sales methods (treatments) on mean weekly sales. Set a = .05. Can we conclude that the different sales methods have different effects on mean weekly sales? 0 Answer is complete and correct. F = 32.6923, p-value = 0.0004: Reject 0 H0: there is a difference 0 in sales methods. (b) Test the null hypothesis Ho that no differences exist between the effects of the salesmen (blocks) on mean weekly sales. Set CI = .05. Can we conclude that the different salesmen have different effects on mean weekly sales? 0 Answer is complete and correct. (c) Use Tukey simultaneous 95 percent condence 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.) 6 Answer is complete but not entirely correct. Method 1 Method 2: [ Method 1 Method 3: [ Method 1 Method 4: [ [ [ [ Method 2 Method 3: Method 2 Method 4: Method 3 Method 4