DATA:

(you will have to convert this data into excel because chegg wouldnt let me paste it, thank you so so much)

PLEASE SHOW ALL THE WORK FOR THE ANSWERS SO WE CAN SEE THE PROCESS BEHIND ANSWERING IT AND PLEASE SHOW HOW THE EXCEL WORK IS DONE.

Question 2 - Discounts and Expected Prices [20 marks] Does the frequency with which a supermarket product is offered at a discount affect the price that customers expect to pay for the product? Does the percent reduction also affect this expectation? These questions were examined by researchers in a study conducted on students enrolled in an introductory statistics course at a large Canadian university. For 10 weeks 160 subjects received information about the products. The treatment conditions corresponded to the number of promotions (1, 3, 5, or 7) during this 10-week period and the percent that the product was discounted (10%, 20%, 30%, and 40%). Ten students were randomly assigned to each of the 4x4 = 16 treatments. The expected price data is contained in worksheet eprice in file Assign3data.xlsx. a) Identify the experimental design. b) Use software to plot the treatment means in an interaction plot and describe the essential features of the data in terms of main effects and interaction. c) Do the data provide sufficient evidence to indicate an interaction between promotions and discount? Conduct the appropriate test. Please provide: Hypotheses Value of test statistic, to two decimal places The critical value for the corresponding test statistic at a=.05 (include degrees of freedom) Exact p-value using software Conclusion; don't simply say reject or do not reject; include a statement with practical meaning d) Based on your answer to part (c), does it make sense to test the effect of promotions or the effect of discount level on the mean expected price? If so, are these effects significant? Justify your answers. e) Plot the residuals against the fitted values. What key model assumptions can be examined and do these appear to be warranted? f) Calculate the Bonferroni margin of error for the confidence intervals based on all the pairwise differences between the 16 treatment means. Assume an overall 95% confidence level. Using the calculated margin of error and a confidence interval approach, test whether the mean expected price is different for the following comparisons For a discount of 10%, 1 promotion versus 3 promotions; For 7 promotions, a 10% discount versus a 20% discount. A D Price 1 Sample 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 B C Promotions Discount 1 1 40 2 1 40 3 1 40 4 1 40 5 1 40 6 1 40 7 1 40 8 1 40 9 1 40 10 1 40 11 1 30 12 1 30 13 1 30 14 1 30 15 1 30 16 1 30 17 1 30 18 1 30 19 30 20 30 21 20 22 20 23 1 20 24 1 20 25 1 20 26 1 20 27 1 20 28 1 20 29 1 20 30 1 20 31 1 10 32 1 10 33 1 10 34 1 10 35 1 10 36 1 10 37 1 10 38 1 10 39 1 10 40 1 10 4.10 4.50 4.47 4.42 4.56 4.69 4.42 4.17 4.31 4.59 3.57 3.77 3.90 4.49 4.00 4.66 4.48 4.64 4.31 4.43 4.94 4.59 4.58 4.48 4.55 4.53 4.59 4.66 4.73 5.24 5.19 4.88 4.78 4.89 4.69 4.96 5.00 4.93 5.10 4.78 42. 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 78 79 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 40 40 40 40 40 40 40 40 40 40 300 30 30 30 30 30 30 30 30 30 20 20 20 20 20 20 20 20 20 20 10 10 10 10 10 10 10 100 4.07 4.13 4.25 4.23 4.57 4.33 4.17 4.47 4.60 4.02. 4.20 3.94 4.20 3.88 4.35 3.99 4.01 4.22 3.70) 4.48 4.88 4.80 4.46 4.73 3.96 4.42 4.30 4.68 4.45 4.56 4.90) 5.15 4.68 4.98 4.66 4.46 | 4.70 4.37 m 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 10 10 40 40 40 40 40 40 40 40 40 40 30 30 30 30 30 30 30 30 30 30 20 20 20 20 20 20 20 20 20 20 10 10 10 10 10 10 10 10 4.69 4.97 3.89 4.18 3.82 4.09 3.94 4.41 4.14 4.15 4.06 3.90 3.90 3.77 3.86 4.10 4.10 3.81 3.97 3.67 4.05 3.67 4.11 4.35 4.17 4.11 4.02 4.41 4.48 3.76 4.66 4.44 4.31 4.36 4.75 4.62 3.74 4.34 4.52 4.37 10 10 40 40 40 40 40 40 40 40 40 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 14 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 119 120 111 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 30 30 30 30 30 30 30 30 30 30 20 20 20 20 20 20 20 20 20 20 10 10 10 10 10 10 10 10 4.40 4.52 3.56 3.91 4.05 3.91 4.11 3.61 3.72 3.69 3.79 3.45 3.45 4.06 3.35 3.67 3.74 3.80 3.90 4.08 3.52 4.03 3.89 4.45 3.80 4.15 4.41 3.75 3.98 4.07 4.21 4.23 4.04 4.22 4.39 3.89 4.26 4.41 4.39 4.52 7 7 7 7 =FDIST(0.43,9,144) j 22 0.917175201 =FINV(0.05,9,144) J K 1.94545019 Question 2 - Discounts and Expected Prices [20 marks] Does the frequency with which a supermarket product is offered at a discount affect the price that customers expect to pay for the product? Does the percent reduction also affect this expectation? These questions were examined by researchers in a study conducted on students enrolled in an introductory statistics course at a large Canadian university. For 10 weeks 160 subjects received information about the products. The treatment conditions corresponded to the number of promotions (1, 3, 5, or 7) during this 10-week period and the percent that the product was discounted (10%, 20%, 30%, and 40%). Ten students were randomly assigned to each of the 4x4 = 16 treatments. The expected price data is contained in worksheet eprice in file Assign3data.xlsx. a) Identify the experimental design. b) Use software to plot the treatment means in an interaction plot and describe the essential features of the data in terms of main effects and interaction. c) Do the data provide sufficient evidence to indicate an interaction between promotions and discount? Conduct the appropriate test. Please provide: Hypotheses Value of test statistic, to two decimal places The critical value for the corresponding test statistic at a=.05 (include degrees of freedom) Exact p-value using software Conclusion; don't simply say reject or do not reject; include a statement with practical meaning d) Based on your answer to part (c), does it make sense to test the effect of promotions or the effect of discount level on the mean expected price? If so, are these effects significant? Justify your answers. e) Plot the residuals against the fitted values. What key model assumptions can be examined and do these appear to be warranted? f) Calculate the Bonferroni margin of error for the confidence intervals based on all the pairwise differences between the 16 treatment means. Assume an overall 95% confidence level. Using the calculated margin of error and a confidence interval approach, test whether the mean expected price is different for the following comparisons For a discount of 10%, 1 promotion versus 3 promotions; For 7 promotions, a 10% discount versus a 20% discount. A D Price 1 Sample 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 B C Promotions Discount 1 1 40 2 1 40 3 1 40 4 1 40 5 1 40 6 1 40 7 1 40 8 1 40 9 1 40 10 1 40 11 1 30 12 1 30 13 1 30 14 1 30 15 1 30 16 1 30 17 1 30 18 1 30 19 30 20 30 21 20 22 20 23 1 20 24 1 20 25 1 20 26 1 20 27 1 20 28 1 20 29 1 20 30 1 20 31 1 10 32 1 10 33 1 10 34 1 10 35 1 10 36 1 10 37 1 10 38 1 10 39 1 10 40 1 10 4.10 4.50 4.47 4.42 4.56 4.69 4.42 4.17 4.31 4.59 3.57 3.77 3.90 4.49 4.00 4.66 4.48 4.64 4.31 4.43 4.94 4.59 4.58 4.48 4.55 4.53 4.59 4.66 4.73 5.24 5.19 4.88 4.78 4.89 4.69 4.96 5.00 4.93 5.10 4.78 42. 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 78 79 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 40 40 40 40 40 40 40 40 40 40 300 30 30 30 30 30 30 30 30 30 20 20 20 20 20 20 20 20 20 20 10 10 10 10 10 10 10 100 4.07 4.13 4.25 4.23 4.57 4.33 4.17 4.47 4.60 4.02. 4.20 3.94 4.20 3.88 4.35 3.99 4.01 4.22 3.70) 4.48 4.88 4.80 4.46 4.73 3.96 4.42 4.30 4.68 4.45 4.56 4.90) 5.15 4.68 4.98 4.66 4.46 | 4.70 4.37 m 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 10 10 40 40 40 40 40 40 40 40 40 40 30 30 30 30 30 30 30 30 30 30 20 20 20 20 20 20 20 20 20 20 10 10 10 10 10 10 10 10 4.69 4.97 3.89 4.18 3.82 4.09 3.94 4.41 4.14 4.15 4.06 3.90 3.90 3.77 3.86 4.10 4.10 3.81 3.97 3.67 4.05 3.67 4.11 4.35 4.17 4.11 4.02 4.41 4.48 3.76 4.66 4.44 4.31 4.36 4.75 4.62 3.74 4.34 4.52 4.37 10 10 40 40 40 40 40 40 40 40 40 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 14 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 119 120 111 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 5 5 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 30 30 30 30 30 30 30 30 30 30 20 20 20 20 20 20 20 20 20 20 10 10 10 10 10 10 10 10 4.40 4.52 3.56 3.91 4.05 3.91 4.11 3.61 3.72 3.69 3.79 3.45 3.45 4.06 3.35 3.67 3.74 3.80 3.90 4.08 3.52 4.03 3.89 4.45 3.80 4.15 4.41 3.75 3.98 4.07 4.21 4.23 4.04 4.22 4.39 3.89 4.26 4.41 4.39 4.52 7 7 7 7 =FDIST(0.43,9,144) j 22 0.917175201 =FINV(0.05,9,144) J K 1.94545019