Expected Price	Promotion	% Discount
4.1	1	40
4.5	1	40
4.47	1	40
4.42	1	40
4.56	1	40
4.69	1	40
4.42	1	40
4.17	1	40
4.31	1	40
4.59	1	40
3.57	1	30
3.77	1	30
3.9	1	30
4.49	1	30
4	1	30
4.66	1	30
4.48	1	30
4.64	1	30
4.31	1	30
4.43	1	30
4.94	1	20
4.59	1	20
4.58	1	20
4.48	1	20
4.55	1	20
4.53	1	20
4.59	1	20
4.66	1	20
4.73	1	20
5.24	1	20
5.19	1	10
4.88	1	10
4.78	1	10
4.89	1	10
4.69	1	10
4.96	1	10
5	1	10
4.93	1	10
5.1	1	10
4.78	1	10
4.07	3	40
4.13	3	40
4.25	3	40
4.23	3	40
4.57	3	40
4.33	3	40
4.17	3	40
4.47	3	40
4.6	3	40
4.02	3	40
4.2	3	30
3.94	3	30
4.2	3	30
3.88	3	30
4.35	3	30
3.99	3	30
4.01	3	30
4.22	3	30
3.7	3	30
4.48	3	30
4.88	3	20
4.8	3	20
4.46	3	20
4.73	3	20
3.96	3	20
4.42	3	20
4.3	3	20
4.68	3	20
4.45	3	20
4.56	3	20
4.9	3	10
5.15	3	10
4.68	3	10
4.98	3	10
4.66	3	10
4.46	3	10
4.7	3	10
4.37	3	10
4.69	3	10
4.97	3	10
3.89	5	40
4.18	5	40
3.82	5	40
4.09	5	40
3.94	5	40
4.41	5	40
4.14	5	40
4.15	5	40
4.06	5	40
3.9	5	40
3.9	5	30
3.77	5	30
3.86	5	30
4.1	5	30
4.1	5	30
3.81	5	30
3.97	5	30
3.67	5	30
4.05	5	30
3.67	5	30
4.11	5	20
4.35	5	20
4.17	5	20
4.11	5	20
4.02	5	20
4.41	5	20
4.48	5	20
3.76	5	20
4.66	5	20
4.44	5	20
4.31	5	10
4.36	5	10
4.75	5	10
4.62	5	10
3.74	5	10
4.34	5	10
4.52	5	10
4.37	5	10
4.4	5	10
4.52	5	10
3.56	7	40
3.91	7	40
4.05	7	40
3.91	7	40
4.11	7	40
3.61	7	40
3.72	7	40
3.69	7	40
3.79	7	40
3.45	7	40
3.45	7	30
4.06	7	30
3.35	7	30
3.67	7	30
3.74	7	30
3.8	7	30
3.9	7	30
4.08	7	30
3.52	7	30
4.03	7	30
3.89	7	20
4.45	7	20
3.8	7	20
4.15	7	20
4.41	7	20
3.75	7	20
3.98	7	20
4.07	7	20
4.21	7	20
4.23	7	20
4.04	7	10
4.22	7	10
4.39	7	10
3.89	7	10
4.26	7	10
4.41	7	10
4.39	7	10
4.52	7	10
3.87	7	10
4.7	7	10

Following their initial analysis, the researchers in the above question are now suspecting that, in addition to the frequency of promotions, the percent (%) reduction may also affect the price that customers are expecting to pay for the product. They conduct a similar study and distributed information about the product for a 10-week period to new sample of 160 students. The treatment conditions corresponded to the number of promotions (1, 3, 5 and 7) that were described and the percent that the product was discounted (10%, 20%, 30% and 40%). Ten students were randomly assigned to each treatment. Data on expected prices for the different groups can be found in the Assig3 Question 2.mtw and Assig3_Data.xlsx data files. (a) Identify the experimental design and the number of treatment combinations? [1 Mark] (b) Plot the residuals against the fitted values. What key model assumptions can be examined and do these appear to be warranted? [2 Marks] (c) Do the data provide sufficient evidence to indicate an interaction between the number of promotions and the percent discounted? Test using a = 0.05 stating the hypotheses. If applicable, explain in plain language what the lack of interaction means in this case. (Make sure to show all the steps) [5 Marks] (d) Examine the interaction plots and explain if it is or isn't consistent with the results in c). [1 Mark] (e) Test the main effect of the number of promotions and main effect of the percent discount on the mean expected price? What do you conclude? (Make sure to show all the steps) [6 Marks] (f) Calculate the Bonferroni margin of error for the confidence intervals based on all pairwise differences between the treatment means. Show your manual calculations and use an overall 95% confidence level. [3 Marks] (g) Using the calculated margin of error and pairwise confidence interval approach in (f) above, test the following statements: (i) For a discount of 10%, 1 promotion vs 3 promotions makes a difference. [1 Mark] (ii) For 1 promotion, a 10% discount vs a 30% discount makes a difference [1 Mark]