i) and ii) please
For some time Eagle Boys pizza chain in Australia has claimed that its pizzas are generally larger than those of Domino's, the biggest pizza chain in the country. For example, advertising material on the company website (http://www.eagleboys.com.au) in 2012 proclaimed "Eagle Boys pizzas have been found to be on average a whole slice larger than Domino's pizzas". To investigate, a group of students in a university Statistics class purchased five "12 inch" pizzas of each of three crust types (deep pan, classic/mid and thin) from both Eagle Boys and Domino's, and measured the diameters of each (in cm). Suppose the data were as given below: Company Domino's Eagle Boys Crust type Deep pan Classic/Mid 27.1, 26.7, 25.8, 26.5, 26.3 27.2, 26.7, 26.7, 26.0, 27.0 28.5, 29.6, 28.5, 28.9, 28.9 29.1, 28.7, 29.4, 29.1, 29.6 28.2, 29.5, 28.9, 28.1, 28.5 30.3, 30.4, 30.1, 29.7, 29.5 Thin Part a) which graphical method would best illustrate main effects and possible interactions? Create such a plot for your data using the command interaction.plot in R. OA. Two histograms OB. A bar chart OC. A plot of means OD. A pie chart OE. A stem-and-leaf plot Part b) The most general model for the data assumes that the diameter of the kth pizza of type j from company i is Yijk = l + ai + Bj + (a)ij + in which is the expected value of y, the overall mean across all the data, a; is the effect of the ith company, i = 1, 2, 3; is the effect of the jth crust type, j= 1, 2, 3, (a)ij is the company-crust interaction effect, and is an independent error, assumed to be from the N(0, o) distribution for some o. Fit the above model to your data using R. Hence, compute the ANOVA table below, providing the requested values (i) and (ii) to 3 decimal places: SS dof MS F (i) 1 Source Company Crust type Interaction 2 2 (ii) Error Total Value for (i) # Value for (ii) For some time Eagle Boys pizza chain in Australia has claimed that its pizzas are generally larger than those of Domino's, the biggest pizza chain in the country. For example, advertising material on the company website (http://www.eagleboys.com.au) in 2012 proclaimed "Eagle Boys pizzas have been found to be on average a whole slice larger than Domino's pizzas". To investigate, a group of students in a university Statistics class purchased five "12 inch" pizzas of each of three crust types (deep pan, classic/mid and thin) from both Eagle Boys and Domino's, and measured the diameters of each (in cm). Suppose the data were as given below: Company Domino's Eagle Boys Crust type Deep pan Classic/Mid 27.1, 26.7, 25.8, 26.5, 26.3 27.2, 26.7, 26.7, 26.0, 27.0 28.5, 29.6, 28.5, 28.9, 28.9 29.1, 28.7, 29.4, 29.1, 29.6 28.2, 29.5, 28.9, 28.1, 28.5 30.3, 30.4, 30.1, 29.7, 29.5 Thin Part a) which graphical method would best illustrate main effects and possible interactions? Create such a plot for your data using the command interaction.plot in R. OA. Two histograms OB. A bar chart OC. A plot of means OD. A pie chart OE. A stem-and-leaf plot Part b) The most general model for the data assumes that the diameter of the kth pizza of type j from company i is Yijk = l + ai + Bj + (a)ij + in which is the expected value of y, the overall mean across all the data, a; is the effect of the ith company, i = 1, 2, 3; is the effect of the jth crust type, j= 1, 2, 3, (a)ij is the company-crust interaction effect, and is an independent error, assumed to be from the N(0, o) distribution for some o. Fit the above model to your data using R. Hence, compute the ANOVA table below, providing the requested values (i) and (ii) to 3 decimal places: SS dof MS F (i) 1 Source Company Crust type Interaction 2 2 (ii) Error Total Value for (i) # Value for (ii)
