Tukey’s Multiple Comparison ExampleBakery products are displayed on one of three shelf levels (bottom, middle, top) in supermarkets. The following monthly sales (in hundreds of items) have been recorded in several supermarkets adopting one ofthe three levels.Analysis of Variance for sales Source DF SS MS F Pshelf 2 1750.33 875.17 119.61 0.000Error 10 73.17 7.32Total 12 1823.50 Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev ----------+---------+---------+------bottom 3 55.833 2.259 (---*--) middle 5 77.600 3.264 (--*-) top 5 52.700 2.255 (--*-) ----------+---------+---------+------Pooled StDev = 2.705 60 70 80Tukey 95% Simultaneous Confidence IntervalsAll Pairwise Comparisons among Levels of shelfIndividual confidence level = 97.93%shelf = bottom subtracted from:shelf Lower Center Upper +---------+---------+---------+---------middle 16.347 21.767 27.186 (---*--)top -8.553 -3.133 2.286 (---*---) +---------+---------+---------+--------- -30 -15 0 15shelf = middle subtracted from:shelf Lower Center Upper +---------+---------+---------+---------top -29.594 -24.900 -20.206 (--*---) +---------+---------+---------+--------- -30 -15 0 151. State why it is appropriate that we use Tukey’s multiple comparison procedure.Since we rejected the null hypothesis that all of the means were equal in the ANOVA (i.e. F=119.61, and the p-value is practically zero), now using Tukey’s is appropriate to find which means are different from the others. 2. Determine which pair(s) of population means are significantly different, according to Tukey’s multiple comparison procedure. Since the CI for bottom-middle is (-27.186,-16.347), then we can conclude with 95%confidence that the average number of bakery items sold when the items are displayed on the bottom shelf is between -27.186 and -16.347 hundred items less than the average number of items sold when the items are displayed on the middleshelf. Similarly, the CI for middle-top indicates that we are 95% confident that that the average number of bakery items sold when the items are displayed on the middle shelf is between 20.206 and 29.594 hundred items more than the average number of items sold when the items are displayed on the top shelf. Since the CIfor bottom-top contains zero, then we conclude that there is no significant difference between these parameters.3. Based on Tukey’s multiple comparison procedure, give a practical conclusion for this follow-up analysis. There is evidence suggests that when displaying bakery items on the middle shelf,that the average number of bakery items sold in a month is larger than when the items are displayed on either the top or bottom
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