Sampling for characterisation. Exercise 1
Objective
To ensure participants are familiar with the basic concepts and practice of sampling and interpretation of the resulting data.
Activity
A small simulated population is to be sampled. The problem is as follows:
The Scene
The district of Ology is in an area where grevillea is grown on farm boundaries. It has been suggested that grevillea production could be intensified - there is certainly a market for the timber - at the same time as introducing some diversity in to the grevillea germplasm. A baseline study to needed identify just how much grevillea is currently grown, who grows it, and what the potential is for increasing it.
Ology consists of three villages with 100, 70 and 30 households. Informal inspection suggests that farm size and numbers of grevillea may be different in each village.
Objectives
1. Estimate the proportion of the households in Ology in each wealth category. (Wealth category is either 1, 2 or 3 defined by the ownership of certain assets).
2. Estimate the average number of grevillea trees per household and the total number in the District.
3. Estimate average length of farm boundary.
4. Estimate the average density of grevillea trees (number of trees per 100m).
5. Test the hypothesis that both the current number of trees and the room for expanding grevillea planting is highest amongst households in wealth category 3.
Method
1. A sample of size 20 is to be taken.
2. Three sampling schemes are:
i. A simple random sample.
ii. A random sample stratified by village.
iii. A systematic sample.
Choose one of these three.
3. ‘Interview’ the household heads of your selected households to find out the wealth category. ‘Measure’ the length of farm boundary and number of grevillea trees.
4. Summarise the data to meet objectives 1-5. Note it is not necessary to do any formal significance testing for objective 5. Simple summaries that show the difference between wealth categories will be sufficient.
The population to sample from
A / 1 / 1 / 2 / 1934 / 55
A / 2 / 2 / 2 / 531 / 15
A / 3 / 3 / 2 / 671 / 31
A / 4 / 4 / 2 / 1550 / 0
A / 5 / 5 / 1 / 109 / 2
A / 6 / 6 / 2 / 1384 / 62
A / 7 / 7 / 3 / 2197 / 143
A / 8 / 8 / 2 / 820 / 68
A / 9 / 9 / 3 / 3027 / 238
A / 10 / 10 / 2 / 96 / 4
A / 11 / 11 / 2 / 211 / 6
A / 12 / 12 / 1 / 329 / 0
A / 13 / 13 / 3 / 1141 / 131
A / 14 / 14 / 3 / 848 / 60
A / 15 / 15 / 1 / 1 / 0
A / 16 / 16 / 2 / 516 / 0
A / 17 / 17 / 3 / 2733 / 124
A / 18 / 18 / 1 / 459 / 12
A / 19 / 19 / 3 / 1120 / 73
A / 20 / 20 / 2 / 852 / 31
A / 21 / 21 / 2 / 646 / 22
A / 22 / 22 / 2 / 1460 / 58
A / 23 / 23 / 2 / 845 / 28
A / 24 / 24 / 1 / 195 / 8
A / 25 / 25 / 1 / 7 / 0
A / 26 / 26 / 2 / 948 / 27
A / 27 / 27 / 1 / 544 / 19
A / 28 / 28 / 2 / 41 / 2
A / 29 / 29 / 3 / 3614 / 492
A / 30 / 30 / 2 / 264 / 24
A / 31 / 31 / 1 / 149 / 2
A / 32 / 32 / 3 / 1410 / 100
A / 33 / 33 / 1 / 646 / 11
A / 34 / 34 / 2 / 456 / 17
A / 35 / 35 / 3 / 693 / 49
A / 36 / 36 / 2 / 401 / 36
A / 37 / 37 / 1 / 423 / 7
A / 38 / 38 / 2 / 858 / 27
A / 39 / 39 / 2 / 76 / 5
A / 40 / 40 / 2 / 1528 / 0
A / 41 / 41 / 1 / 80 / 2
A / 42 / 42 / 2 / 977 / 46
A / 43 / 43 / 2 / 1740 / 158
A / 44 / 44 / 2 / 680 / 23
A / 45 / 45 / 3 / 2407 / 180
A / 46 / 46 / 2 / 326 / 23
A / 47 / 47 / 3 / 1186 / 68
A / 48 / 48 / 1 / 9 / 0
A / 49 / 49 / 2 / 10 / 0
A / 50 / 50 / 3 / 5436 / 263
A / 51 / 51 / 2 / 886 / 0
A / 52 / 52 / 2 / 392 / 24
A / 53 / 53 / 3 / 1399 / 95
A / 54 / 54 / 3 / 3479 / 200
A / 55 / 55 / 3 / 2896 / 197
A / 56 / 56 / 2 / 319 / 13
A / 57 / 57 / 1 / 244 / 3
A / 58 / 58 / 2 / 858 / 61
A / 59 / 59 / 3 / 2722 / 116
A / 60 / 60 / 2 / 2421 / 220
A / 61 / 61 / 2 / 2308 / 115
A / 62 / 62 / 2 / 743 / 39
A / 63 / 63 / 3 / 1224 / 59
A / 64 / 64 / 2 / 990 / 58
A / 65 / 65 / 2 / 454 / 12
A / 66 / 66 / 2 / 913 / 27
A / 67 / 67 / 2 / 1012 / 40
A / 68 / 68 / 1 / 401 / 14
A / 69 / 69 / 2 / 1144 / 114
A / 70 / 70 / 2 / 598 / 46
A / 71 / 71 / 3 / 721 / 0
A / 72 / 72 / 2 / 1504 / 88
A / 73 / 73 / 2 / 943 / 49
A / 74 / 74 / 2 / 279 / 11
A / 75 / 75 / 1 / 419 / 11
A / 76 / 76 / 2 / 725 / 32
A / 77 / 77 / 2 / 1193 / 62
A / 78 / 78 / 3 / 3030 / 133
A / 79 / 79 / 2 / 12 / 0
A / 80 / 80 / 2 / 718 / 42
A / 81 / 81 / 2 / 302 / 15
A / 82 / 82 / 1 / 212 / 0
A / 83 / 83 / 2 / 988 / 0
A / 84 / 84 / 3 / 1616 / 0
A / 85 / 85 / 2 / 824 / 48
A / 86 / 86 / 2 / 2273 / 133
A / 87 / 87 / 2 / 453 / 19
A / 88 / 88 / 1 / 125 / 4
A / 89 / 89 / 3 / 2011 / 111
A / 90 / 90 / 1 / 230 / 4
A / 91 / 91 / 2 / 920 / 61
A / 92 / 92 / 2 / 1518 / 94
A / 93 / 93 / 2 / 1440 / 130
A / 94 / 94 / 2 / 726 / 48
A / 95 / 95 / 1 / 295 / 5
A / 96 / 96 / 3 / 4380 / 252
A / 97 / 97 / 2 / 93 / 5
A / 98 / 98 / 2 / 271 / 24
A / 99 / 99 / 3 / 2878 / 0
A / 100 / 100 / 2 / 484 / 14
B / 1 / 101 / 3 / 2211 / 106
B / 2 / 102 / 2 / 549 / 39
B / 3 / 103 / 3 / 2847 / 305
B / 4 / 104 / 2 / 1157 / 42
B / 5 / 105 / 3 / 1670 / 125
B / 6 / 106 / 2 / 1882 / 125
B / 7 / 107 / 2 / 28 / 1
B / 8 / 108 / 3 / 5340 / 0
B / 9 / 109 / 2 / 1840 / 55
B / 10 / 110 / 2 / 2838 / 105
B / 11 / 111 / 2 / 968 / 48
B / 12 / 112 / 1 / 715 / 21
B / 13 / 113 / 3 / 2307 / 230
B / 14 / 114 / 2 / 197 / 0
B / 15 / 115 / 2 / 40 / 1
B / 16 / 116 / 2 / 130 / 7
B / 17 / 117 / 3 / 1504 / 72
B / 18 / 118 / 3 / 1059 / 46
B / 19 / 119 / 2 / 60 / 3
B / 20 / 120 / 2 / 744 / 74
B / 21 / 121 / 2 / 994 / 0
B / 22 / 122 / 2 / 322 / 14
B / 23 / 123 / 2 / 1158 / 68
B / 24 / 124 / 2 / 186 / 16
B / 25 / 125 / 3 / 464 / 0
B / 26 / 126 / 2 / 150 / 6
B / 27 / 127 / 3 / 825 / 37
B / 28 / 128 / 3 / 100 / 6
B / 29 / 129 / 1 / 824 / 0
B / 30 / 130 / 2 / 1805 / 95
B / 31 / 131 / 1 / 57 / 1
B / 32 / 132 / 2 / 1031 / 33
B / 33 / 133 / 3 / 1374 / 98
B / 34 / 134 / 1 / 150 / 0
B / 35 / 135 / 1 / 53 / 1
B / 36 / 136 / 1 / 305 / 10
B / 37 / 137 / 2 / 538 / 16
B / 38 / 138 / 2 / 1222 / 39
B / 39 / 139 / 2 / 275 / 0
B / 40 / 140 / 3 / 1776 / 140
B / 41 / 141 / 2 / 1810 / 120
B / 42 / 142 / 2 / 106 / 3
B / 43 / 143 / 3 / 4112 / 0
B / 44 / 144 / 2 / 2072 / 62
B / 45 / 145 / 2 / 2063 / 60
B / 46 / 146 / 3 / 1442 / 108
B / 47 / 147 / 2 / 2319 / 68
B / 48 / 148 / 2 / 336 / 17
B / 49 / 149 / 2 / 100 / 0
B / 50 / 150 / 2 / 864 / 37
B / 51 / 151 / 2 / 973 / 81
B / 52 / 152 / 2 / 1160 / 50
B / 53 / 153 / 3 / 708 / 0
B / 54 / 154 / 3 / 2831 / 353
B / 55 / 155 / 2 / 1686 / 73
B / 56 / 156 / 1 / 891 / 17
B / 57 / 157 / 3 / 3991 / 460
B / 58 / 158 / 3 / 1443 / 0
B / 59 / 159 / 2 / 76 / 5
B / 60 / 160 / 2 / 2511 / 73
B / 61 / 161 / 2 / 262 / 0
B / 62 / 162 / 1 / 34 / 0
B / 63 / 163 / 3 / 3069 / 306
B / 64 / 164 / 3 / 4799 / 0
B / 65 / 165 / 3 / 869 / 81
B / 66 / 166 / 3 / 451 / 19
B / 67 / 167 / 3 / 1407 / 0
B / 68 / 168 / 2 / 992 / 39
B / 69 / 169 / 3 / 2282 / 228
B / 70 / 170 / 2 / 1089 / 54
C / 1 / 171 / 3 / 2962 / 193
C / 2 / 172 / 3 / 849 / 45
C / 3 / 173 / 2 / 2020 / 59
C / 4 / 174 / 1 / 430 / 6
C / 5 / 175 / 2 / 46 / 2
C / 6 / 176 / 1 / 278 / 4
C / 7 / 177 / 2 / 105 / 3
C / 8 / 178 / 2 / 453 / 25
C / 9 / 179 / 2 / 121 / 0
C / 10 / 180 / 3 / 3241 / 0
C / 11 / 181 / 2 / 583 / 44
C / 12 / 182 / 2 / 685 / 34
C / 13 / 183 / 2 / 901 / 39
C / 14 / 184 / 2 / 318 / 22
C / 15 / 185 / 3 / 1688 / 93
C / 16 / 186 / 3 / 2366 / 0
C / 17 / 187 / 2 / 402 / 0
C / 18 / 188 / 3 / 3891 / 265
C / 19 / 189 / 3 / 112 / 8
C / 20 / 190 / 2 / 378 / 18
C / 21 / 191 / 3 / 2186 / 0
C / 22 / 192 / 2 / 660 / 41
C / 23 / 193 / 2 / 872 / 54
C / 24 / 194 / 2 / 100 / 0
C / 25 / 195 / 3 / 1615 / 89
C / 26 / 196 / 3 / 1023 / 52
C / 27 / 197 / 3 / 958 / 130
C / 28 / 198 / 2 / 774 / 40
C / 29 / 199 / 1 / 135 / 0
C / 30 / 200 / 2 / 140 / 0