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, 1' Sales Method, 1'. A B C 1 32 29 30 2 32 30 23 3 23 25 23 4 25 24 24 Analysis of Variance Sum of Mean Seurce DF Squares Square 1' Ratio Model 5 106.50000 21.3000 19.6615 Error 6 6.50000 1.0833 Prob > F c. Total 11 113.00000 22.3033 0.0012* Effect II'ests Sum of Source Nparm 131" Squares 1" Ratio Prob > 5' Method 3 3 87.000000 26.7692 0.0007* Salesman 2 2 19.500000 9.0000 0.0150 Least Squares Means Estimates Method Estimate Salesman Estimate 1 30.333333 A 29.250000 2 30.000000 B 27.000000 3 25.333333 C 26.250000 4 24.333333 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 0.3498366 0.39 0.9777 2.60855 3.275220 1 3 5.000000 0.3498366 5.38 0.0043\" 2.05812 7.941830 1 4 6.000000 0.3498366 7.06 0.0017* 3.05812 8.941880 2 3 4.666667 0.3498366 5.49 0.0061* 1.72478 7.608550 2 4 5.666667 0.3498366 6.67 0.0023\" 2.72478 8.608550 3 4 1.000000 0.3498366 1.18 0.6613 l.94188 3.941830 (3) Test the null hypothesis so 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? 9 Answer is complete and correct. F = 26.7692, p-value = 0 0007. H0: there is a difference a in sales methods. Reject 0 (b) Test the null hypothesis an that no differences exist between the effects of the salesmen {blocks} on mean weekly sales. Set a = .05. Can we conclude that the different salesmen have different effects on mean weekly sales? 0 Answer is complete and correct. F = 9.0000. p-value = 0 0156' Reject 9 H0: salesman do 9 have an effecton sales. (c) Use Tukey simultaneous 95 percent confidence intervals to make pairwise comparisons of the sales method effects on mean weekly sales. Which sales methodis) maximize mean weekly sales? {Round your answers to 3 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: [ i [ Method 2 Method 4: Method 3 Method 4: A consumer preference study compares the effects of three different bottle designs (A, B, and C.) on sales of a popular fabric softener. A completely randomized design is employed. Specically, 15 supermarkets of equal sales potential are selected, and 5 of these supermarkets are randomly assigned to each bottle design. The number of bottles sold in 24 hours at each supermarket is recorded. The data obtained are displayed in the following table. Bottle Design Study Data A B C 19 32 26 14 31 21 19 31 2? 18 29 23 13 32 23 The Excel output of a one-way ANOVA of the Bottle Design Study Data is shown below. SUMMARY Groups Count Sum Average Variance Design A 5 83 16.6 8.3 Design B 5 155 31.0 1.5 Design C 5 120 24.0 6.0 ANOVA Source of. Variation SS df Ms 1' PValue F orit Between Groups 513.5333 2 259.266".II 49.23 1.64EOE 3.38529 Within Groups 63.2 12.0 5.2630 Total 531.7333 14 (a) Test the null hypothesis that #11. mg, and ye are equal by setting a = .05. Based on this test, can we conclude that bottle designs A. B. and C have different effects on mean daily sales? (Round your answers to 2 decimal places} 9 Answer is not complete. p~va|ue = 0.000 @ Reject 0 HO: bottle design does 0 have an impact on sales. (b) Consider the pairwise differences ,uB M, #c ,uA , and m;- ,uB. Find a point estimate of and a Tukey simultaneous 95 percent confidence interval for each pairwise difference. Interpret the results in practical terms. Which bottle design maximizes mean daily sales? (Round your answers to 2 decimal places. Negative amounts should be Indicated by a minus sign.) 9 Answer is not complete. Point estimate Condence Interval pB pA: . [ . ] p0 pA: . [ . 1 p0 -pB: . [ - 1 0 Answer is complete and correct. Bottle design B o maximlzes sales. (c) Find a 95 percent condence interval for each of the treatment means #5113, and pic. Interpret these intervals. [Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.) 9 Answer is not complete. Condence Interval HA: [ pB: [ . p0: [