Table 1: Summary statistics of sales (in 1000's of $ per day) for the five stores. Table 2: The overall ANOVA table for comparison of mean sales between the five stores. Table 3: The results of Tukey multiple comparisons for pairwise difference in mean sales between stores. Question 1 (Seven parts; 36 marks in total) The managers in a certain shopping mall wanted to compare the sales of 5 clothing stores (A, B, C, D, and E) in the mall, particularly on Saturdays. They determined the total daily sales (in thousands of dollars) of each store on 6 randomly selected Saturdays during the year. Assume all the assumptions for the required analyses are satisfied. Use the SPSS output in Tables 1-3 below to answer parts (a) to (g). Parameters are defined as follows: A= the mean of total sales per day in Store A B= the mean of total sales per day in Store B C= the mean of total sales per day in Store C D= the mean of total sales per day in Store D E= the mean of total sales per day in Store E (a) (5 marks) At the 5% significance level, carry out the most appropriate test to determine if there is any difference in mean sales between the five stores. SHOW ALL STEPS. (b) (1 mark) What is the best estimate for the common or pooled standard deviation of the 5 populations? (c) (2 marks) Based on the SPSS output for Tukey's multiple comparisons performed at the 95\% confidence level (Table 3), construct a means comparisons diagram to illustrate the results. (d) (10 marks) At the 95\% confidence level, perform the Bonferroni method of multiple comparisons to determine which pairs of stores have different mean sales. SHOW ALL STEPS, including compilation of the results in a matrix and giving the conclusion both in a means comparisons diagram and in words. Note: You only have to calculate the margin of error once since sample sizes are equal for all groups. (e) (2 marks) Compare the means comparisons diagrams you constructed in parts (c) and (d). Do they show the same results? Regardless of whether they show the same or different result, state whether they could have shown different results, explaining the reasons for potential differences. (f) (8 marks) The managers of the mall were interested in comparing the sales of Stores A and B, which are on the west side of the mall near the food court, with the sales of Stores C and D, which are on the west side of the mall. Develop a linear combination (contrast) to test the hypothesis that there is a difference in the mean sales between Stores A and B (combined) in comparison with Stores C and D (combined). Then, test this contrast at the 5% significance level. SHOW ALL STEPS. (g) (8 marks) Store E is at the far northern end of the mall away from the busy area. Develop a linear combination (contrast) to test the hypothesis that there is a difference in the mean sales between Store E (by itself) in comparison with Stores A and B (combined). Then, test this contrast at the 5% significance level. SHOW ALL STEPS of the hypothesis test