6) A drugstore manager needs to purchase adequate supplies of various brands of toothpaste to meet the ongoing demands of its customers. In particular, the company is interested in estimating the proportion of its customers who favor the country's leading brand of toothpaste, Crest. To evaluate the toothpaste brand preference of the customers, the drugstore manager randomly selects 200 customers and records their preference. The data appear in the Toothpaste worksheet in the Confidence Interval HW data workbook on Moodle. a) Draw a column chart of the number of customers who prefer each of the different brands of toothpaste. Interpret the column chart for the drugstore manager. b) Find a 95% upper confidence limit on the proportion of customers who prefer Crest. Interpret this interval for the drugstore manager in the context of estimating the proportion of customers who prefer Crest. c) Find 95% confidence intervals on the proportion of customers who prefer Colgate and Aquafresh. Using these intervals, can you conclude more customers prefer one of these brands than the other? Summary Statistics Mean 100.5 Std Dev 57.879185 Std Err Mean 4.0926764 Upper 95% Mean 108.57058 Lower 95% Mean 92.42942 N 200 Confidence Intervals Parameter Estimate Lower CI Upper CI 1-Alpha Mean 100.5 92.42942 108.5706 0.950 Std Dev 57.87918 52.7084 64.18367 0.950 Customer 1 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 42 43 44 45 46 47 48 49 50 Preference Colgate Mentadent Crest Colgate Aquafresh Others Others Aquafresh Crest Others Crest Crest Colgate Colgate Others Colgate Crest Colgate Others Colgate Others Aquafresh Crest Crest Mentadent Others Crest Mentadent Others Colgate Others Crest Mentadent Others Crest Others Others Others Crest Mentadent Crest Colgate Aquafresh Crest Others Others Mentadent Others Mentadent Crest 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 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Others Others Crest Others Crest Crest Mentadent Others Colgate Mentadent Crest Mentadent Others Colgate Crest Crest Colgate Others Colgate Crest Mentadent Crest Colgate Colgate Crest Crest Crest Aquafresh Aquafresh Crest Colgate Crest Others Colgate Crest Others Crest Others Crest Crest Mentadent Mentadent Others Others Colgate Crest Crest Others Colgate Mentadent 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 Others Aquafresh Colgate Others Mentadent Crest Mentadent Colgate Colgate Aquafresh Crest Crest Aquafresh Crest Others Aquafresh Others Aquafresh Others Crest Crest Crest Colgate Others Others Aquafresh Others Colgate Crest Mentadent Others Others Crest Others Aquafresh Others Others Crest Mentadent Others Crest Aquafresh Crest Mentadent Mentadent Crest Others Others Others Crest 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 Colgate Aquafresh Crest Others Mentadent Crest Others Crest Mentadent Crest Crest Others Crest Others Mentadent Colgate Others Others Others Others Crest Others Mentadent Colgate Crest Others Mentadent Others Others Mentadent Crest Mentadent Crest Colgate Colgate Aquafresh Crest Others Others Others Others Colgate Crest Aquafresh Aquafresh Others Colgate Others Others Crest 6) A drugstore manager needs to purchase adequate supplies of various brands of toothpaste to meet the ongoing demands of its customers. In particular, the company is interested in estimating the proportion of its customers who favor the country's leading brand of toothpaste, Crest. To evaluate the toothpaste brand preference of the customers, the drugstore manager randomly selects 200 customers and records their preference. The data appear in the Toothpaste worksheet in the Confidence Interval HW data workbook on Moodle. a) Draw a column chart of the number of customers who prefer each of the different brands of toothpaste. Interpret the column chart for the drugstore manager. b) Find a 95% upper confidence limit on the proportion of customers who prefer Crest. Interpret this interval for the drugstore manager in the context of estimating the proportion of customers who prefer Crest. c) Find 95% confidence intervals on the proportion of customers who prefer Colgate and Aquafresh. Using these intervals, can you conclude more customers prefer one of these brands than the other? Summary Statistics Mean 100.5 Std Dev 57.879185 Std Err Mean 4.0926764 Upper 95% Mean 108.57058 Lower 95% Mean 92.42942 N 200 Confidence Intervals Parameter Estimate Lower CI Upper CI 1-Alpha Mean 100.5 92.42942 108.5706 0.950 Std Dev 57.87918 52.7084 64.18367 0.950 Customer 1 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 42 43 44 45 46 47 48 49 50 Preference Colgate Mentadent Crest Colgate Aquafresh Others Others Aquafresh Crest Others Crest Crest Colgate Colgate Others Colgate Crest Colgate Others Colgate Others Aquafresh Crest Crest Mentadent Others Crest Mentadent Others Colgate Others Crest Mentadent Others Crest Others Others Others Crest Mentadent Crest Colgate Aquafresh Crest Others Others Mentadent Others Mentadent Crest 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 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Others Others Crest Others Crest Crest Mentadent Others Colgate Mentadent Crest Mentadent Others Colgate Crest Crest Colgate Others Colgate Crest Mentadent Crest Colgate Colgate Crest Crest Crest Aquafresh Aquafresh Crest Colgate Crest Others Colgate Crest Others Crest Others Crest Crest Mentadent Mentadent Others Others Colgate Crest Crest Others Colgate Mentadent 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 Others Aquafresh Colgate Others Mentadent Crest Mentadent Colgate Colgate Aquafresh Crest Crest Aquafresh Crest Others Aquafresh Others Aquafresh Others Crest Crest Crest Colgate Others Others Aquafresh Others Colgate Crest Mentadent Others Others Crest Others Aquafresh Others Others Crest Mentadent Others Crest Aquafresh Crest Mentadent Mentadent Crest Others Others Others Crest 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 Colgate Aquafresh Crest Others Mentadent Crest Others Crest Mentadent Crest Crest Others Crest Others Mentadent Colgate Others Others Others Others Crest Others Mentadent Colgate Crest Others Mentadent Others Others Mentadent Crest Mentadent Crest Colgate Colgate Aquafresh Crest Others Others Others Others Colgate Crest Aquafresh Aquafresh Others Colgate Others Others Crest