A studyr investigated the effect of shelf placement on supermarket sales of Mellow Moments, a brand of Instant coffee. The study ran over a period of fourteen weekdays. and on a given day the coffee brand was shelved In cne of three different heights: knee, waist, oreye level. The assignment ofshelf position to day was at random. On each day, the sales of Mellow Moments {In $ 100) were recorded and were as follows: Knee Level 5.58 6.34 7.33 4.90 Waist Level 6.57 7.69 8.37 7.68 7.57 Eye Level 6.51 7.42 6.20 7.79 6.54 Box plots displaying the data are shown below: My sales of Mellow Mom-nu co'l'lle by supermarket shelf I Sales in 1005 of Dolor: T I T Knee Waist Eye Shelf Height Part a]: TRUE or FALSE: If applying the analysis ofvaliance [ANOWQ to these data, we must assume... I) The sample mean sales for the three shelf heights are equal. 0 A. This 0 B. False II) The daily sales from each shelf height are from a Normal dlstnhutlon. o A. This 0 5. False Ill) The daily sales for each shelf height are independent. 0 A. This 0 5. False iv) The sample standard deviations of the sales for the different shelf heights are Independent. 0 A. True 0 5. False v} The daily sales for the different shelf heights are independent. 0 A. Tnle O 5. False Part b] A table summarizing the data is given below. Provide the missing standard deviation (to three decimal places]: Height Sample size Mean Standard deviation Knee Level 4 6.100 Waist Level 5 7.9T6 [1.459 Eye Level 5 101 2 [1.613 Pan (:1 Complete the ANOVA table below. giving answers to three decimal places {please Keep at least 6 decimal places in all intermediate steps and use the non-rounded values for all calculations): Source of variation of Sum of Squares Mean Squares F-ratlo Treatment 2 1.875 Total 13 13.302 Part d] Taking that the underfylng assumptions of ANOVA hold and that the approach will be applied. what is the estimate of the common variance of the daily sales for the three shelf heights? (Give your answer to three decimal places). Pan e} Which of the following lnferences can be made when testing the null hypothesis that the three shelf heights give the same mean dail}l sales. on. Since the observed F statistic is less than Puma\" we do not reject the null hypothesis that the three shelf heights give the same mean daily sales. 0 3. Since the observed F statistic is greaterthan Emma\" we do not reject the null hypothesis that the three sheir heights give the same mean daily sales. 00. Since the observed F statistic Is less than Fe-tl.us,2,11 we can reject the null hypothesis that the three shelf heights give the same mean daily sales. 0 D. Since the observed F statistic is greater than Fix-0.05.2.11 we can reiect the null hypothesis that the three shelf heights give the same mean daily sales
