(6 points} A study 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 dayr the coffee brand was shelved in one of three different heights: knee, waist. or eye level. The assignment of shelf position to day was at random. On each day, the sales of Mellow Moments {in $ 100) were recorded and were as follows: Knee Level 6.55 5.?6 6.52 T02 Waist Level 180 142 8.09 8.13 T27 Eye Level ?.45 5.55 7.20 6.04 8.23 Box plots displaying the data are shown below. lily sales of Hallow Moments C'll In; supermarket shelf! Sales in 1005 of Dolars 6.5 T 0 1.5 8.0 5.0 Knee Waist Eye Shelf Height: Part a] TRUE or FALSE: If applying the analysis of variance (ANOVA) to these data. we must assume... i) The sample mean sales forthe three shelf heights are equal. 0 A. True 0 B. False ii) The daily sales from each shelf height are li'om a Normal distribution. 0 A. True 0 3. False iii) The daily sales for each shelf height are independent. 0 A. True 0 El. False iv) The sample standard deviations of the sales for the different shelf heights are independent. 0 A. True 0 3. False iv) The sample standard deviations of the sales for the different shelf heights are independent. 0 A. True Q B. False v] The daily sales for the dilferent sherf heights are independent. 0 A. True 0 5. False Part bi Atable summanzing the data is given below. Provide the missing standard deviation (to three decimal places): Height Sample size Mean Standard deviation Knee Level 4 5.487 Waist Level 5 ?.?52 0.401 Eye Level 5 "[104 0.859 Part e] Complete the ANDVA table below, giving answers 0 three decimal places (please keep at least 5 decimal places in all intermediate steps and use the non-rounded values for all calculations): Source of Variation df Sum of Squares Mean Squares Fratio Treatment 2 Error 11 Total 13 8.004 Part oi Taking that the underlying assumptions ofANOVA hold and that the approach will be applied, what is the estimate of the common vanance of the daily sales forthe three sherf heights? (Give your answer to three decimal places). Part a] Which of the following inferences can be made when testing the null hypothesis that the three shelf heights give the same mean daily sales. OA. Since the observed F statistic is greater than F :I}.IJE,2l11 we can reject the null hypothesis that the three sherf heights give the same mean daily sales. Q E. Since the observed F statistic is greater than F $1.353!\" we do not reject the null hypothesis that the three shelf heights give the same mean daily sales. 0 G. Since the observed F statistic is less than Fal'n we can reject the null hypothesis that the three shelf heights give the same mean daily sales. 0 o. Since the observed F statistic is less than Fungal-Au we do not reject the null hypothesis that the three shelf heights give the same mean daily sales