Use probability proportional to size and systematic sampling to select 4 EBs fro
ID: 3357799 • Letter: U
Question
Use probability proportional to size and systematic sampling to select 4 EBs from 12 EBs below, and then select 30 households from each selected EB. Let 511 be the random start.
EB
Number of households
1
297
2
321
3
105
4
399
5
122
6
403
7
312
8
328
9
327
10
98
11
104
12
184
a)Select the four EBs.
b)Find the first stage, second stage and overall probability for selecting households for each of the selected EB.
c)If the mean values corresponding to the selected EBs (in that order) are 4.5., 3.7, 2.8 and 3.3, find Upps and place a bound on the error of estimation (B).
EB
Number of households
1
297
2
321
3
105
4
399
5
122
6
403
7
312
8
328
9
327
10
98
11
104
12
184
Explanation / Answer
Probability of Selection of EB
EB
Number of House Holds
c.f.
Probability
Y
X
1
297
297
0.099
2
321
618
0.107
3
105
723
0.035
4
399
1122
0.133
5
122
1244
0.040666667
6
403
1647
0.134333333
7
312
1959
0.104
8
328
2287
0.109333333
9
327
2614
0.109
10
98
2712
0.032666667
11
104
2816
0.034666667
12
184
3000
0.061333333
Total
3000
1
(a) Selection of sample of size 4 (i.e. Selection of four EB's by Simple Random Sampling without Replaement)
Note that, the random number generated in excel worksheet using commad [=randbetween(1,3000)]
Random Number
Selected Unit in the sample
first unit (EB) of the sample
210
1
second unit (EB) of the sample
1490
6
third unit (EB) of the sample
918
4
fourth unit (EB) of the sample
2871
12
(b) Selection of 30 house holds by sysetematic sampling (Second Stage)
the polpulation for second stage sample
1
297
4
399
6
403
12
184
Total
1283 (N)
The population size N= 1283
Sample size n= 30
sampling interval k=N/n 42.76666667 = 43(approx)
Random start i= 511 (given)
The house hold selected in the Sample are given as below
Serial Number
Sample House holds
1
511
2
554
3
597
4
640
5
683
6
726
7
769
8
812
9
855
10
898
11
941
12
984
13
1027
14
1070
15
1113
16
1156
17
1199
18
1242
19
2
20
45
21
88
22
131
23
174
24
217
25
260
26
303
27
346
28
389
29
432
30
475
EB
Number of House Holds
c.f.
Probability
Y
X
1
297
297
0.099
2
321
618
0.107
3
105
723
0.035
4
399
1122
0.133
5
122
1244
0.040666667
6
403
1647
0.134333333
7
312
1959
0.104
8
328
2287
0.109333333
9
327
2614
0.109
10
98
2712
0.032666667
11
104
2816
0.034666667
12
184
3000
0.061333333
Total
3000
1
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