Question

8. Does the location of an item on the grocery shelf impact its sales? To find out, a grocery store targeted a specific product, and placed it on one of three shelf levels (top, middle or bottom) and observed its daily sales. The experiment lasted 12 days, with the product placed on each of the 3 shelf levels for 4 days. Its daily sales are recorded as follows: Shelf Level Top Daily Sales 75, 57, 99, 85 78, 89, 82, 103 60, 62, 81, 77 Middle Bottom You are given a = 77, 172. (a) (4 points) State the assumption(s) that must be made about the distributions of daily sales of the product at the 3 different shelf levels in order to carry out ANOVA. (b) (8 points) Using the above data, perform an ANOVA to test if there is a significant difference in the average daily sales of this product based on its shelf level. Use a = 0.05.

Answer 1

ay The assumptions basis to analysis of variance are ! a) The variables considered follow a normal dist within each set of combinations. b) The several popna sampled have the same standard deviation, c) The healment effect are additive,

as solution. Here the factor of variation is shelf levels ( Top. Middle Boltom). we set up the hypothesis. Null hypothesis : Mo: Mi=112=113 - je all shelf levels are equally effective Alternative Hypothesis: At least too of the means - are not equal. level of signit cance = x=0.05. It is given, ni= n2 = n3 = 4, N = Ni+ M2 + 3 = 12 K=3.. 8 x = 77,172 shelf level Daily sales Total Top 75, 57, 99, 85 T. = 316 73=99856 Middle 78, 89, 82, 103 T2. = 352 T2² = 123904 Bottom 60, 62, 81, 77 Tg. = 280 T3²= 78400 Total = G7 948 ET= 302160) ROW S S.CR-SS) = x = 74172 G = EE X = 316 +352280 = 948 correction factor CCF). G2 - 898704 4892 Total s. s. CT.S.S) RSS - CF 4172-94892 = 2280 C.F. Treatment s... (34) = T . 2 30216074892

Treatment sis est) = 648 Errors.s (52) = T.S.S. - S.S.T = 2280- 648 Ess = 1632 ANOVA Tables I dof. MSS Source of sum of ranation squares (2) Treatment (shelf levels) 648 vanance Ratio (F) (3) (4) = (2) (3) 3-1=2 324 1.7867 Emor 1632 11-2=9 181.3333 Total 2280 12-1 = 11 The critical Crabulated) value 820.05 level of significance for (2, 9) def 4.2564. & is since the computed value of test statistic is less than critical value it lies in the acceptance. region. Hence we accept Ho, at 5% lend of significance & conclude asi confidence that the treatment (Shelf levels) Top, Medium, Bothom are not significantly