15-6: Consider the following set of data:
x1 10 8 11 7 10 11 6
x2 50 45 37 32 44 51 42
y 103 85 115 73 97 102 65
In: Statistics and Probability
A study aimed to determine if grapefruit juice has beneficial effects on the pharmacokinetics of oral digoxin, a drug often prescribed for heart ailments. Seven healthy non-smoking volunteers participated in the study. Subjects took digoxin with water for 2 weeks, no digoxin for 2 weeks, and then digoxin with grapefruit juice for 2 weeks. The peak plasma digoxin concentrations (Cmax; ng/mL) when subjects took digoxin under the two conditions are given in the following table:
Subject 1 2 3 4 5 6 7
Water 2.34 2.46 1.87 3.09 5.59 4.05 6.21
Grapefruit Juice 3.03 3.46 1.97 3.81 3.07 2.62 3.44
Decrease -0.69 -1.00 -0.10 -0.72 2.52 1.43 2.77
While small, note that the sample size was chosen carefully by the authors. In their paper they state that “assuming an � level of 0.05, a sample size of seven subjects has a power of 85% to detect a 25% change in digoxin Cmax”. Lower values of Cmax are better since they imply that digoxin is available in the body for longer. Is there any evidence that grapefruit juice increases the effectiveness of oral digoxin, by decreasing Cmax? (a) Identify one issue in the design of this experiment that undermines being able to use the data to answer this question. How could the design be improved? [2 marks]
(b) Suppose mew is the true mean decrease in digoxin Cmax with grapefruit compared to water. Define the null and alternative hypotheses for this study in symbols. [1 mark]
(c) We have two sets of Cmax measurements, one for water and one for grapefruit. Briefly explain why we work with the differences rather than carrying out a twosample t-test to compare the treatments. [1 mark]
(d) The seven differences in Cmax have mean 0.601 ng/mL with standard deviation 1.609 ng/mL. Use these values to test the hypotheses in (b). What do you conclude? [2 marks]
(e) How many of the seven subjects had a lower Cmax value with grapefruit juice? Use this to find the P-value for a sign test of whether grapefruit juice tends to lower Cmax. What do you conclude? [2 marks]
(f) For a sign test from seven subjects, what is the minimum number of reductions in Cmax needed to give evidence of an effect at the 5% level? [1 mark]
In: Statistics and Probability
I dont know what to do: Is there a significant difference between drug type and mean relative-change* of Cholesterol from screening to follow up?
* Relative Change = (Follow up - Initial) / Initial
| Patient ID | Drug | Stomach Pain | Sex | Age | Height | Systolic BP | Diastolic BP | Exercise | Coffee Consumption | Alcohol Consumption | Weight | Weight3 | Cholesterol | Cholesterol3 | Triglycerides | Triglycerides3 | HDL | HDL3 | LDL | LDL3 |
| 1 | B | Yes | F | 22 | 67.13 | 124 | 78 | 180 | 1 | > 2 | 138 | 145 | 197 | 182 | 152 | 135 | 43 | 34 | 151.6 | 145.8 |
| 2 | B | Yes | M | 22 | 63 | 122 | 70 | 0 | 2 | < 2 | 115 | 122 | 181 | 151 | 59 | 57 | 60 | 48 | 120.1 | 102.1 |
| 3 | B | No | F | 22 | 72 | 124 | 80 | 90 | 0 | < 2 | 190 | 190 | 190 | 169 | 117 | 86 | 41 | 37 | 147.1 | 130.6 |
| 4 | A | Yes | M | 22 | 69 | 120 | 70 | 120 | 5 | > 2 | 115 | 105 | 131 | 133 | 54 | 72 | 58 | 67 | 72.1 | 64.8 |
| 5 | B | Yes | M | 25 | 73 | 138 | 92 | 40 | 2 | > 2 | 160 | 165 | 172 | 166 | 93 | 139 | 49 | 40 | 121.5 | 123.8 |
| 6 | B | Yes | M | 22 | 67.5 | 100 | 72 | 0 | 0 | < 2 | 150 | 165 | 233 | 229 | 176 | 144 | 42 | 38 | 188.2 | 188.7 |
| 7 | A | Yes | M | 23 | 73 | 128 | 78 | 0 | 2 | < 2 | 154 | 150 | 194 | 148 | 79 | 80 | 49 | 26 | 143.7 | 120.7 |
| 8 | A | No | M | 24 | 71.5 | 128 | 74 | 90 | 0 | < 2 | 185 | 187 | 155 | 148 | 89 | 73 | 45 | 50 | 108.6 | 96.8 |
| 9 | A | Yes | F | 23 | 73.5 | 124 | 82 | 60 | 1 | > 2 | 178 | 166 | 234 | 175 | 307 | 88 | 28 | 28 | 201.1 | 145.6 |
| 10 | A | Yes | M | 22 | 72.25 | 130 | 88 | 40 | 0 | 0 | 158 | 163 | 201 | 203 | 88 | 112 | 50 | 40 | 149.6 | 161.2 |
| 11 | A | No | M | 26 | 73 | 130 | 86 | 0 | 1 | < 2 | 188 | 195 | 258 | 276 | 299 | 199 | 30 | 21 | 223.2 | 251.8 |
| 12 | A | No | M | 22 | 64.25 | 120 | 74 | 0 | 0 | > 2 | 150 | 150 | 212 | 228 | 52 | 61 | 69 | 60 | 142.2 | 167 |
| 13 | B | Yes | M | 22 | 64.25 | 120 | 74 | 0 | 4 | 0 | 123 | 131 | 137 | 165 | 158 | 147 | 29 | 39 | 105.5 | 123.6 |
| 14 | B | No | F | 27 | 65 | 100 | 68 | 180 | 2 | > 2 | 138 | 133 | 285 | 229 | 98 | 89 | 69 | 61 | 214.4 | 166.6 |
| 15 | A | No | M | 22 | 59 | 124 | 84 | 180 | 0 | > 2 | 143 | 140 | 218 | 172 | 101 | 96 | 46 | 21 | 170.4 | 149.5 |
| 16 | B | Yes | F | 24 | 67.5 | 122 | 68 | 210 | 1 | < 2 | 139 | 151 | 167 | 152 | 71 | 91 | 51 | 37 | 114.9 | 113.5 |
| 17 | A | Yes | F | 22 | 71.5 | 118 | 70 | 60 | 0 | < 2 | 156 | 155 | 170 | 158 | 81 | 91 | 42 | 40 | 126.7 | 116.5 |
| 18 | A | Yes | M | 22 | 69 | 125 | 76 | 180 | 0 | < 2 | 150 | 154 | 157 | 140 | 86 | 88 | 37 | 34 | 118.6 | 104.6 |
| 19 | A | Yes | M | 24 | 68 | 122 | 74 | 100 | 5 | > 2 | 135 | 128 | 215 | 176 | 71 | 53 | 62 | 46 | 151.9 | 129.2 |
| 20 | A | No | M | 25 | 74 | 134 | 88 | 180 | 0 | < 2 | 219 | 220 | 194 | 207 | 71 | 130 | 40 | 33 | 152.9 | 171.9 |
| 21 | A | No | F | 28 | 71 | 110 | 80 | 60 | 2 | > 2 | 173 | 173 | 207 | 231 | 107 | 145 | 53 | 47 | 152.3 | 181.7 |
| 22 | A | Yes | M | 22 | 68.5 | 116 | 84 | 280 | 0 | 0 | 151 | 165 | 198 | 199 | 80 | 126 | 44 | 46 | 152.7 | 151 |
| 23 | A | Yes | M | 23 | 75.5 | 124 | 73 | 60 | 1 | 0 | 182 | 183 | 189 | 262 | 47 | 230 | 50 | 31 | 138.2 | 227.3 |
| 24 | A | Yes | M | 24 | 70 | 124 | 72 | 360 | 0 | < 2 | 161 | 163 | 216 | 203 | 95 | 121 | 35 | 28 | 179.5 | 173.1 |
| 25 | B | Yes | F | 22 | 72 | 126 | 88 | 120 | 0 | 0 | 176 | 173 | 212 | 173 | 140 | 88 | 43 | 35 | 166.8 | 136.6 |
| 26 | B | Yes | F | 26 | 72.5 | 138 | 82 | 0 | 0 | < 2 | 177 | 175 | 175 | 169 | 77 | 78 | 46 | 52 | 127.8 | 115.8 |
| 27 | B | Yes | F | 23 | 72 | 120 | 68 | 60 | 1 | < 2 | 174 | 197 | 158 | 172 | 57 | 126 | 34 | 30 | 123.1 | 140 |
| 28 | B | No | F | 20 | 74 | 118 | 76 | 0 | 2 | 0 | 234 | 217 | 115 | 146 | 95 | 110 | 26 | 33 | 87.5 | 111.2 |
| 29 | B | No | F | 28 | 66 | 138 | 82 | 120 | 0 | 0 | 150 | 160 | 228 | 224 | 480 | 373 | 29 | 28 | 191.3 | 190 |
| 30 | A | Yes | F | 23 | 74 | 124 | 76 | 60 | 0 | < 2 | 149 | 150 | 164 | 164 | 94 | 92 | 43 | 44 | 119.5 | 118.5 |
| 31 | B | Yes | M | 22 | 70 | 118 | 72 | 0 | 0 | < 2 | 156 | 160 | 149 | 149 | 155 | 65 | 37 | 29 | 109.5 | 119 |
| 32 | A | Yes | F | 23 | 71.5 | 124 | 70 | 180 | 3 | < 2 | 168 | 170 | 211 | 183 | 63 | 60 | 52 | 44 | 158 | 138 |
| 33 | B | Yes | F | 22 | 73 | 122 | 76 | 0 | 0 | < 2 | 182 | 170 | 191 | 185 | 99 | 101 | 39 | 39 | 150.4 | 144.4 |
| 34 | B | No | F | 40 | 75 | 128 | 80 | 0 | 5 | > 2 | 217 | 230 | 277 | 243 | 240 | 218 | 71 | 28 | 202.2 | 211.5 |
| 35 | B | No | M | 22 | 65 | 128 | 82 | 120 | 1 | < 2 | 190 | 201 | 178 | 191 | 52 | 77 | 41 | 56 | 136.2 | 133.8 |
| 36 | A | Yes | F | 25 | 69 | 124 | 78 | 150 | 5 | < 2 | 159 | 154 | 157 | 112 | 93 | 71 | 41 | 38 | 114.5 | 72.9 |
| 37 | A | No | M | 22 | 73 | 126 | 73 | 180 | 0 | 0 | 191 | 199 | 151 | 155 | 44 | 94 | 42 | 44 | 108.3 | 109.5 |
| 38 | A | No | M | 24 | 59.5 | 122 | 72 | 100 | 0 | 0 | 140 | 140 | 209 | 165 | 71 | 71 | 41 | 42 | 166.9 | 121.9 |
| 39 | B | No | F | 23 | 71 | 116 | 72 | 120 | 0 | 0 | 183 | 186 | 209 | 147 | 95 | 124 | 37 | 29 | 170.5 | 116 |
| 40 | B | Yes | F | 26 | 71 | 132 | 78 | 90 | 0 | 0 | 162 | 167 | 197 | 216 | 47 | 64 | 43 | 43 | 153.2 | 172 |
| 41 | B | No | M | 29 | 69.5 | 130 | 82 | 0 | 3 | < 2 | 181 | 169 | 226 | 208 | 126 | 86 | 38 | 36 | 186 | 170.6 |
| 42 | B | No | F | 30 | 70 | 112 | 72 | 0 | 5 | < 2 | 196 | 199 | 127 | 139 | 116 | 69 | 32 | 31 | 93.1 | 106.9 |
| 43 | A | No | M | 25 | 65.5 | 120 | 72 | 180 | 2 | > 2 | 141 | 143 | 180 | 162 | 85 | 93 | 41 | 46 | 137.6 | 114.5 |
| 44 | B | No | F | 25 | 74 | 117 | 77 | 0 | 2 | 0 | 230 | 217 | 117 | 146 | 95 | 110 | 25 | 33 | 87.5 | 111.2 |
| 45 | A | Yes | M | 24 | 70 | 122 | 76 | 100 | 5 | > 2 | 135 | 128 | 215 | 177 | 71 | 53 | 62 | 46 | 151.9 | 129.2 |
In: Math
Scroll the bottom arrows to see the whole table. if I make it any smaller you will not be able to see the numbers clearly: Is there a relationship between the relative-change* in weight and the relative-change* in Cholesterol level from screening to follow up for patients taking Drug A?
* Relative Change = (Follow up - Initial) / Initial
| Patient ID | Drug | Stomach Pain | Sex | Age | Height | Systolic BP | Diastolic BP | Exercise | Coffee Consumption | Alcohol Consumption | Weight | Weight3 | Cholesterol | Cholesterol3 | Triglycerides | Triglycerides3 | HDL | HDL3 | LDL | LDL3 |
| 1 | B | Yes | F | 22 | 67.13 | 124 | 78 | 180 | 1 | > 2 | 138 | 145 | 197 | 182 | 152 | 135 | 43 | 34 | 151.6 | 145.8 |
| 2 | B | Yes | M | 22 | 63 | 122 | 70 | 0 | 2 | < 2 | 115 | 122 | 181 | 151 | 59 | 57 | 60 | 48 | 120.1 | 102.1 |
| 3 | B | No | F | 22 | 72 | 124 | 80 | 90 | 0 | < 2 | 190 | 190 | 190 | 169 | 117 | 86 | 41 | 37 | 147.1 | 130.6 |
| 4 | A | Yes | M | 22 | 69 | 120 | 70 | 120 | 5 | > 2 | 115 | 105 | 131 | 133 | 54 | 72 | 58 | 67 | 72.1 | 64.8 |
| 5 | B | Yes | M | 25 | 73 | 138 | 92 | 40 | 2 | > 2 | 160 | 165 | 172 | 166 | 93 | 139 | 49 | 40 | 121.5 | 123.8 |
| 6 | B | Yes | M | 22 | 67.5 | 100 | 72 | 0 | 0 | < 2 | 150 | 165 | 233 | 229 | 176 | 144 | 42 | 38 | 188.2 | 188.7 |
| 7 | A | Yes | M | 23 | 73 | 128 | 78 | 0 | 2 | < 2 | 154 | 150 | 194 | 148 | 79 | 80 | 49 | 26 | 143.7 | 120.7 |
| 8 | A | No | M | 24 | 71.5 | 128 | 74 | 90 | 0 | < 2 | 185 | 187 | 155 | 148 | 89 | 73 | 45 | 50 | 108.6 | 96.8 |
| 9 | A | Yes | F | 23 | 73.5 | 124 | 82 | 60 | 1 | > 2 | 178 | 166 | 234 | 175 | 307 | 88 | 28 | 28 | 201.1 | 145.6 |
| 10 | A | Yes | M | 22 | 72.25 | 130 | 88 | 40 | 0 | 0 | 158 | 163 | 201 | 203 | 88 | 112 | 50 | 40 | 149.6 | 161.2 |
| 11 | A | No | M | 26 | 73 | 130 | 86 | 0 | 1 | < 2 | 188 | 195 | 258 | 276 | 299 | 199 | 30 | 21 | 223.2 | 251.8 |
| 12 | A | No | M | 22 | 64.25 | 120 | 74 | 0 | 0 | > 2 | 150 | 150 | 212 | 228 | 52 | 61 | 69 | 60 | 142.2 | 167 |
| 13 | B | Yes | M | 22 | 64.25 | 120 | 74 | 0 | 4 | 0 | 123 | 131 | 137 | 165 | 158 | 147 | 29 | 39 | 105.5 | 123.6 |
| 14 | B | No | F | 27 | 65 | 100 | 68 | 180 | 2 | > 2 | 138 | 133 | 285 | 229 | 98 | 89 | 69 | 61 | 214.4 | 166.6 |
| 15 | A | No | M | 22 | 59 | 124 | 84 | 180 | 0 | > 2 | 143 | 140 | 218 | 172 | 101 | 96 | 46 | 21 | 170.4 | 149.5 |
| 16 | B | Yes | F | 24 | 67.5 | 122 | 68 | 210 | 1 | < 2 | 139 | 151 | 167 | 152 | 71 | 91 | 51 | 37 | 114.9 | 113.5 |
| 17 | A | Yes | F | 22 | 71.5 | 118 | 70 | 60 | 0 | < 2 | 156 | 155 | 170 | 158 | 81 | 91 | 42 | 40 | 126.7 | 116.5 |
| 18 | A | Yes | M | 22 | 69 | 125 | 76 | 180 | 0 | < 2 | 150 | 154 | 157 | 140 | 86 | 88 | 37 | 34 | 118.6 | 104.6 |
| 19 | A | Yes | M | 24 | 68 | 122 | 74 | 100 | 5 | > 2 | 135 | 128 | 215 | 176 | 71 | 53 | 62 | 46 | 151.9 | 129.2 |
| 20 | A | No | M | 25 | 74 | 134 | 88 | 180 | 0 | < 2 | 219 | 220 | 194 | 207 | 71 | 130 | 40 | 33 | 152.9 | 171.9 |
| 21 | A | No | F | 28 | 71 | 110 | 80 | 60 | 2 | > 2 | 173 | 173 | 207 | 231 | 107 | 145 | 53 | 47 | 152.3 | 181.7 |
| 22 | A | Yes | M | 22 | 68.5 | 116 | 84 | 280 | 0 | 0 | 151 | 165 | 198 | 199 | 80 | 126 | 44 | 46 | 152.7 | 151 |
| 23 | A | Yes | M | 23 | 75.5 | 124 | 73 | 60 | 1 | 0 | 182 | 183 | 189 | 262 | 47 | 230 | 50 | 31 | 138.2 | 227.3 |
| 24 | A | Yes | M | 24 | 70 | 124 | 72 | 360 | 0 | < 2 | 161 | 163 | 216 | 203 | 95 | 121 | 35 | 28 | 179.5 | 173.1 |
| 25 | B | Yes | F | 22 | 72 | 126 | 88 | 120 | 0 | 0 | 176 | 173 | 212 | 173 | 140 | 88 | 43 | 35 | 166.8 | 136.6 |
| 26 | B | Yes | F | 26 | 72.5 | 138 | 82 | 0 | 0 | < 2 | 177 | 175 | 175 | 169 | 77 | 78 | 46 | 52 | 127.8 | 115.8 |
| 27 | B | Yes | F | 23 | 72 | 120 | 68 | 60 | 1 | < 2 | 174 | 197 | 158 | 172 | 57 | 126 | 34 | 30 | 123.1 | 140 |
| 28 | B | No | F | 20 | 74 | 118 | 76 | 0 | 2 | 0 | 234 | 217 | 115 | 146 | 95 | 110 | 26 | 33 | 87.5 | 111.2 |
| 29 | B | No | F | 28 | 66 | 138 | 82 | 120 | 0 | 0 | 150 | 160 | 228 | 224 | 480 | 373 | 29 | 28 | 191.3 | 190 |
| 30 | A | Yes | F | 23 | 74 | 124 | 76 | 60 | 0 | < 2 | 149 | 150 | 164 | 164 | 94 | 92 | 43 | 44 | 119.5 | 118.5 |
| 31 | B | Yes | M | 22 | 70 | 118 | 72 | 0 | 0 | < 2 | 156 | 160 | 149 | 149 | 155 | 65 | 37 | 29 | 109.5 | 119 |
| 32 | A | Yes | F | 23 | 71.5 | 124 | 70 | 180 | 3 | < 2 | 168 | 170 | 211 | 183 | 63 | 60 | 52 | 44 | 158 | 138 |
| 33 | B | Yes | F | 22 | 73 | 122 | 76 | 0 | 0 | < 2 | 182 | 170 | 191 | 185 | 99 | 101 | 39 | 39 | 150.4 | 144.4 |
| 34 | B | No | F | 40 | 75 | 128 | 80 | 0 | 5 | > 2 | 217 | 230 | 277 | 243 | 240 | 218 | 71 | 28 | 202.2 | 211.5 |
| 35 | B | No | M | 22 | 65 | 128 | 82 | 120 | 1 | < 2 | 190 | 201 | 178 | 191 | 52 | 77 | 41 | 56 | 136.2 | 133.8 |
| 36 | A | Yes | F | 25 | 69 | 124 | 78 | 150 | 5 | < 2 | 159 | 154 | 157 | 112 | 93 | 71 | 41 | 38 | 114.5 | 72.9 |
| 37 | A | No | M | 22 | 73 | 126 | 73 | 180 | 0 | 0 | 191 | 199 | 151 | 155 | 44 | 94 | 42 | 44 | 108.3 | 109.5 |
| 38 | A | No | M | 24 | 59.5 | 122 | 72 | 100 | 0 | 0 | 140 | 140 | 209 | 165 | 71 | 71 | 41 | 42 | 166.9 | 121.9 |
| 39 | B | No | F | 23 | 71 | 116 | 72 | 120 | 0 | 0 | 183 | 186 | 209 | 147 | 95 | 124 | 37 | 29 | 170.5 | 116 |
| 40 | B | Yes | F | 26 | 71 | 132 | 78 | 90 | 0 | 0 | 162 | 167 | 197 | 216 | 47 | 64 | 43 | 43 | 153.2 | 172 |
| 41 | B | No | M | 29 | 69.5 | 130 | 82 | 0 | 3 | < 2 | 181 | 169 | 226 | 208 | 126 | 86 | 38 | 36 | 186 | 170.6 |
| 42 | B | No | F | 30 | 70 | 112 | 72 | 0 | 5 | < 2 | 196 | 199 | 127 | 139 | 116 | 69 | 32 | 31 | 93.1 | 106.9 |
| 43 | A | No | M | 25 | 65.5 | 120 | 72 | 180 | 2 | > 2 | 141 | 143 | 180 | 162 | 85 | 93 | 41 | 46 | 137.6 | 114.5 |
| 44 | B | No | F | 25 | 74 | 117 | 77 | 0 | 2 | 0 | 230 | 217 | 117 | 146 | 95 | 110 | 25 | 33 | 87.5 | 111.2 |
| 45 | A | Yes | M | 24 | 70 | 122 | 76 | 100 | 5 | > 2 | 135 | 128 | 215 | 177 | 71 | 53 | 62 | 46 | 151.9 | 129.2 |
In: Math
A researcher designs an experiment to measure the effectiveness of the new ointment in treating shingles. Singles is a very serious, painful disease. A medical doctor examines the sixteen voluntary subjects. She finds four of subjects each with a moderate case of shingles and of these two are females and two are males. The other twelve subjects each have a severe case of shingles and of these eight are females and 4 are males. All subjects are aged 50 to 60, and except for shingles are in good health. For the standard ointment treatment, the doctor knows that females tend to respond better to the treatment than males do.
The statistician in charge of designing the experiment decides to conduct a double blind experiment using two treatment groups of subjects. Neither the doctor nor any of the subjects will know who receives which ointment. The control group will receive the standard ointment treatment for which the effectiveness is well known. The experimental group will receive new ointment. The two ointments are in identical tubes and both ointments appear identical. The subjects will receive detailed instructions on the application of the ointment. Each subject will apply the same amount of ointment three times a day, which is the recommended dosage of the standard ointment. They will have weekly follow up visits over two months after which the experiment will end. During weekly follow-up visits the doctor will assess if patients are correctly applying the ointment and use a Likert scale from 0, 1, 2, 3, to 4 to judge the severity of the rash with 0 indicating no rash and 4 a very severe rash.
Because males and females tend to respond differently to the standard treatment, the researcher must block males and females into a block of all males and another block of all females. For the male block, he randomly assigns one male with moderate case of shingles to new ointment treatment and the other male to the standard ointment treatment. Likewise, he randomly randomly assigns two of males with a severe case to new ointment treatment and the other two to the standard ointment treatment. Similarly, for the female block, he randomly assigns one moderate case to each of the two treatments. In addition, he randomly assigns four of females with a severe case to new ointment treatment and the other four to the standard ointment treatment. He runs the experiment for two months. For both males and females within each block and between each block, he compares how well and how fast the new ointment and the standard ointment work.
A.Why did the design not include a placebo?
B. Does the lack of a placebo put the results into question?
C. Do you see any design flaws in the original design?
Assume individuals with other serious health problems like cancer have a much harder time curing shingles than otherwise healthy individuals and that generally people older than 70 are also harder to cure.
4) When the experiment is replicated, should this additional information be taken into account? Describe how this would affect the design of the experiment.
In: Statistics and Probability
Hypothesis Testing and Confidence Intervals
The Reliable Housewares store manager wants to learn more about the purchasing behavior of its
"credit" customers. In fact, he is speculating about four specific cases shown below (a) through (d) and
wants you to help him test their accuracy.
b. The true population proportion of credit customers who live in an urban area exceeds 55%
i. Using the dataset provided in Files perform the hypothesis test for each of the above speculations (a) through (d) in order to see if there is an statistical evidence to support the manager’s belief. In each case,
oUse the
Seven Elements of a Test of Hypothesis, in Section 7.1 of your textbook (on or about Page 361) or the Six Steps of Hypothesis Testing I have identified in the addendum.
oUse α=2%for all your analyses,
oExplain your conclusion in simple terms,
oIndicate which hypothesis is the“claim”,
o Compute the p-value,
o Interpret your results,
ii.Follow your work in (i) with computing a 98% confidence interval for each of the variables
described in (a) though (d). Interpret these intervals.
iii.
Write an executive summary for the Reliable Housewares store manager about your analysis,
distilling down the results in a way that would be understandable to someone who does not
know statistics. Clear explanations and interpretations are critical.
| Location | Income ($1000) |
Size | Years | Credit Balance ($) |
| Rural | 30 | 2 | 12 | 3,159 |
| Rural | 31 | 2 | 4 | 1,864 |
| Rural | 37 | 1 | 20 | 2,731 |
| Rural | 27 | 1 | 19 | 2,477 |
| Rural | 33 | 2 | 12 | 2,514 |
| Rural | 44 | 1 | 7 | 2,995 |
| Rural | 42 | 2 | 19 | 3,020 |
| Rural | 30 | 1 | 14 | 2,583 |
| Rural | 50 | 2 | 11 | 3,605 |
| Rural | 35 | 1 | 11 | 3,121 |
| Rural | 27 | 2 | 1 | 2,921 |
| Rural | 30 | 2 | 14 | 3,067 |
| Rural | 22 | 4 | 16 | 3,074 |
| Rural | 53 | 1 | 7 | 2845 |
| Suburban | 32 | 4 | 17 | 5,100 |
| Suburban | 50 | 5 | 14 | 4,742 |
| Suburban | 66 | 4 | 10 | 4,764 |
| Suburban | 63 | 4 | 13 | 4,965 |
| Suburban | 62 | 6 | 13 | 5,678 |
| Suburban | 55 | 7 | 15 | 5,301 |
| Suburban | 54 | 6 | 14 | 5,573 |
| Suburban | 67 | 4 | 13 | 5,037 |
| Suburban | 22 | 3 | 18 | 3,899 |
| Suburban | 39 | 2 | 18 | 2,972 |
| Suburban | 54 | 3 | 9 | 3,730 |
| Suburban | 23 | 6 | 18 | 4,127 |
| Suburban | 61 | 2 | 14 | 4,273 |
| Suburban | 46 | 5 | 13 | 4,820 |
| Suburban | 66 | 4 | 20 | 5,149 |
| Suburban | 74 | 7 | 12 | 5394 |
| Suburban | 66 | 7 | 14 | 5036 |
| Urban | 54 | 3 | 12 | 4,016 |
| Urban | 55 | 2 | 9 | 4,070 |
| Urban | 40 | 2 | 7 | 3,348 |
| Urban | 51 | 3 | 16 | 4,110 |
| Urban | 25 | 3 | 11 | 4,208 |
| Urban | 48 | 4 | 16 | 4,219 |
| Urban | 65 | 3 | 12 | 4,214 |
| Urban | 55 | 6 | 15 | 4,412 |
| Urban | 21 | 2 | 18 | 2,448 |
| Urban | 37 | 5 | 5 | 4,171 |
| Urban | 21 | 3 | 16 | 3,623 |
| Urban | 41 | 7 | 18 | 4,828 |
| Urban | 48 | 2 | 8 | 3,866 |
| Urban | 34 | 5 | 5 | 3,586 |
| Urban | 67 | 5 | 1 | 5,345 |
| Urban | 55 | 6 | 10 | 5,370 |
| Urban | 52 | 2 | 11 | 3,890 |
| Urban | 62 | 3 | 2 | 4,705 |
| Urban | 64 | 2 | 6 | 4,157 |
| Urban | 29 | 4 | 4 | 3,890 |
| Urban | 39 | 4 | 15 | 4,183 |
| Urban | 26 | 7 | 17 | 4,603 |
| Urban | 44 | 6 | 5 | 3962 |
| Urban | 25 | 3 | 15 | 3442 |
In: Statistics and Probability
Question 8
Hypothesis Test - Terminology
Match terms to descriptions Question 8 options:
a) The hypothesis expressing a claim involving one of =, ≤ (at
most), or ≥ (at least) and requiring no (null) action.
b) The hypothesis expressing a claim involving one of ≠, >, or
< and requiring action.
c) The sign of the critical value of a a 1-tail test with upper
reject region is
d) Greek letter denoting the population standard deviation
e) For an upper tail test, the probability of an equal or greater
test statistic.
f) Greek letter denoting the population mean
g) The sign of the critical value of a 1-tail test with lower
reject region is
h) Rejecting H0 when H0 is actually false
i) The risk as a probability that we are willing to take of
rejecting H0 when it is actually true.
j) Greek letter denoting the population proportion
k) Failure to reject H0 when H0 is actually false
l) Rejection of the null hypothesis when H0 is actually true
M) The value of the test statistic where the pvalue = significance
level α.
Match with the following:
1) H0
2) HA
3) pvalue
4) alpha α
5) Critical value
6) Type 1 error
7) Type 2 error
8) Not an error
9) Negative
10) Positive
11) μ
12) π
13) σ
14) No answer fits
In: Statistics and Probability
Group A has three scores, 12, 39, 42. Group B has three scores, 49, 46, 14. Group C has three scores, 49, 39, 32. Calculate the grand mean (round to two digits).
QUESTION 2
Group A has three scores, 36, 50, 47. Group B has three scores, 17, 40, 18. Group C has three scores, 40, 29, 18. Calculate MS error (Mean squared error for the error term). Round to one digit.
QUESTION 3
Group A has three scores, 17, 31, 39. Group B has three scores, 23, 36, 29. Group C has three scores, 48, 16, 13. Calculate SS total (the total sums of squares). Round to two digits.
In: Statistics and Probability
Question 1
A small manufacturing company recently instituted Six Sigma
training for its employees. Two
methods of training were offered: online and traditional classroom.
Management was interested
in whether the division in which employees worked affected their
choice of method.
Below is a table summarizing the data.
|
Sales |
Quality |
Operations |
Total |
|
|
Traditional |
16 |
10 |
8 |
34 |
|
Online |
35 |
23 |
44 |
104 |
|
Total |
51 |
33 |
52 |
136 |
(a) What is the probability that an employee chose online
training? [2 marks]
(b) What is the probability that an employee is in the quality
division and chose online training?
[2 marks]
(c) What is the probability that an employee chose online training
given that he or she is in the
sales division? [2 marks]
(d) What is the probability that an employee chose online training
or is from the sales division?
[3 marks]
(e) Are the events “chose online training” and “from the sales
division” independent? Give
reason for your answer. [2 marks]
Question 2
A game consists of flipping a fair coin twice and counting the
number of heads that appear. The
distribution for the number of heads, X, is given by: P(X
= 0) = ¼; P(X =1) =1/2; P(X = 2) =¼
A player receives $0 for no heads, $2 for 1 head, and $5 for 2
heads (there is no cost to play the
game). Calculate the expected amount of winnings ($). [2 marks]
Question 3
Internet service providers (ISP) need to resolve customer problems
as quickly as possible. For
one ISP, past data indicate that the likelihood is 0.80 that
customer calls regarding Internet
service interruptions are resolved within one hour. Out of the next
10 customer calls about
interrupted service,
(a) What is the probability that at least 7 will be resolved within
one hour? [4 marks]
(b) How many customers would be expected to have their service
problems resolved within one
hour? [1 mark]
Question 4
A mail-order company receives an average of five orders per 500
solicitations. If it sends out 100
advertisements, find the probability of receiving at least two
orders. [Hint: Use the Poisson
distribution]. Ensure that you define the variable of interest.
Question 5
An airline knows from experience that the distribution of the
number of suitcases that get lost
each week on a certain route is approximately normal with μ = 15.5
and σ = 3.6. What is the
probability that during a given week the airline will lose between
10 and 20 suitcases?
Question 6
Assume that the heights of women are normally distributed with a
mean of 62.2 inches and a
standard deviation of 2.3 inches. Find the third quartile that
separates the bottom 75% from the
top 25%. Total 4 marks
In: Statistics and Probability
Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year old baby and the weight y of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females. x (lb) 20 24 22 25 20 15 25 21 17 24 26 22 18 19 y (lb) 126 124 122 124 130 120 145 130 130 130 130 140 110 115 Σx = 298; Σy = 1,776; Σx2 = 6,486; Σy2 = 226,362; Σxy = 37,990 (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your answers for least-squares estimates to three decimal places.) x = y = b = ŷ = + x (b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = r2 = What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) % (d) If a female baby weighs 17 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) lb
In: Statistics and Probability