Question

has three packaging designs for a new product. In a trial evaluation, 15 stones from similar and supplied the new item. Only one package design, however, is used in A company marketing areas are selected any one store. The number of sales during the first 45 days following the introduction of the product are given below DesignI Design II Design IlI 240 255 285 260 360 410 205 280 340 360 370 280 340 450 (a) Write down the statistical model for the above design defining all terms used in the model (4) (b) Can the company conclude that the package design has an effect on sales? use a 0.05 (10) (c) Use LSD at 5% to perform a pairwise comparison and make appropriate recommendations (6) Total 20

urgent

Answer 1

a). For the given data the linear model is given by yij = μ + α¡ + 티j , î=1,2,3 (design) ;je 1,2,3,4,5 (row) Where, yij is response sales form jth row receiving ith treatment(design), u is general mean effect, a is effect due to ith design, Ei 1S random error ij b). null hypothesis: There is no significant effect due to design on the sales after performing ANOVA (CRD) in SPSS, the results are given below ANOVA values Mean Square Sum of Squares 19763.333 48970.000 68733.333 df Si 2.421 Between Grou Within Groups Total 9881.667 131 4080.833 From the above ANOVA table, it can be observed that p-value(sig.) is - 0.131 which is greater than 0.05 Hence, we do not reject the null hypothesis and conclude that there is no significant effect due to design on the sales at 5% level of significance c). The LSD multiple comparison test results are given belovw Multiple Comparisons LSD 95% Confidence Interval Mean Difference Upper Bound Lower Bound 143.03 176.03 33.03 121.03 03 55.03 design Std. Error 40.402 40.402 40.402 40.402 40.402 40.402 Si 198 050 198 430 050 430 55.000 88.000 55.000 33.000 88.000 33.000 33.03 03 143.03 55.03 176.03 121.03 From the above table, all the p-values are greater than or cqual to 0.05 There is a significant difference between all pairs of means of designs