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 32 29 30 2 32 30 28 3 28 25 23 4 25 24 23 ANOVA: Two-Factor without Replication SUMMARY Count Sum Average Variance Method 1 3 91 30.3333 2.3333 Method 2 3 90 30 4 Method 3 3 76 25.3333 6.3333 Method 4 3 72 24 1 Salesman A 4 117 29.25 11.5833 Salesman B 4 108 27 8.6667 Salesman C 4 104 26 12.6667 ANOVA Source of Variation SS df MS F P-Value F crit Treatments 93.5833 3 31.1944 36.2258 0.0003 4.7571 Blocks 22.1667 2 11.0833 12.8710 0.0068 5.1433 Error 5.1667 6 0.8611 Total 120.9167 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 = 36.23, p-value = .000; H0: there is a in sales methods. (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 = 12.87, p-value = .007; H0: salesman 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