Latihan soal MPC II Praktikum
Murthy #354
9.2 In a sample survey for estimating the number of standards of
pepper in a tehsil having 72 villages, a sample of 12 villages
was selected with SRS WOR and from each sample village 5
clusters of 20 fields each were drawn with SRS WOR. Data on
number of clusters in the sample village and on the number
of standards in the sample cluster are given in Table 9.7.
Sample No of
Village Clusters
1
2
3
4
5
6
7
8
9
10
11
12
27
24
14
116
25
118
147
26
91
171
86
88
Number of standards in
sample cluster
1
2
3
4
5
430 402 363 975 389
586 1234 100 368 344
1164 546 3060 1724 1274
693 218 836 1218 575
191 270 4502 4184 243
1036 1333 1179 728 1957
1555 254 950 382 355
910 452 129 122 243
340
0
92
28 340
57
59
0
0
21
159
45 242 1075 539
84 462 147
16
10
Estimate the unbiased total number of standards in the tehsil
and obtain its RSE by estimating its unbiased variance
9.3 For estimating the average household expenditure 𝑌̅ in a
region, it is proposed to adopt a two stage sampling design,
where villages in the first stage and households in the second
stage would be selected with SRS WR. To help in planning
the survey, a pilot survey was conducted and it was found
that a) estimate of 𝑌̅ is 50 b) estimate of between-village
variation 𝜎𝑏 2 = 85.5 c) estimate of between-household
variation within villages 𝜎𝑤 2 = 36.5 d) cost of travel, etc 𝐶1 =
𝑅𝑠 . 9 e) cost of survey per household 𝐶2 = 𝑅𝑒 . 1 . Using this
information and assuming the overhead cost to be 𝑅𝑠 . 1000 ,
determine the optimum number of sample villages and
number of households to be sampled per sample village,
when the total cost is fixed at (i) 𝑅𝑠 . 5000 (ii) 𝑅𝑠 . 10000 (iii)
𝑅𝑠 . 50000 . Also calculate the minimum RSE’s attained in the
three cases.
9.6 It is proposed to draw a sample of n clusters of M units each
from a population of N clusters an a sub sample of m units
from each sample cluster using SRS WR at both the stage for
estimating the mean per unit of a specified characteristic.
(i)Assuming the cost function to be of the form
C=Co+C1n+C2mn
Determine the optimum values of m and n when C is fixed
at C’
(ii)Given that C’=1000, Co=300, C1=9, and C2=1 (in rupees),
find the optimum values of m and n using the following
analysis of variance table
Table 9.10 ANALYSIS OF VARIANCE FOR THE STUDY VARIABLE
Source of
variation
(1)
Degrees of
freedom
(2)
Sum of squares
Mean squares
(3)
(4)
20 ∑(𝑌̅𝑖 − 𝑌̅)2
180.9
90
Between
clusters
89
Within clusters
1710
𝑖=1
90 20
∑ ∑(𝑌𝑖𝑗 − 𝑌̅𝑖 )
2
49.5
𝑖=1 𝑗=1
90 20
Total
1799
2
∑ ∑(𝑌𝑖𝑗 − 𝑌̅)
56.0
𝑖=1 𝑗=1
(total number of clusters : 90, number of units in a cluster : 20)
9.7 For estimating the total yield of paddy (Y) in a district, a
stratified two stage sampling design was adopted, where 4
villages were selected from each stratum, with PPS WR, size
being geographical area, and 4 plots were drawn from each
sample villages circular systematically for ascertaining the
yield of paddy. Using the information given in 9.11, estimate
unbiased Y and obtain an estimate of its RSE.
Table 9.11 YIELD OF PADDY FOR THE SAMPLE PLOTS
Stratum
Sample
village
Invers of
probability
Total no
of plots
Yield of paddy
(in kilogrammes)
28
14
240
76
1
(5)
104
108
100
346
2
(6)
182
64
115
350
3
(7)
148
132
50
157
4
(8)
87
156
172
119
(1)
1
(2)
1
2
3
4
(3)
440.21
660.43
31.50
113.38
(4)
2
1
2
3
4
21.00
16.80
24.76
49.99
256
288
222
69
124
123
264
300
111
177
78
114
135
106
144
68
216
138
55
111
3
1
2
3
4
67.68
339.14
100.00
68.07
189
42
134
161
110
80
121
243
281
61
212
116
120
118
174
314
114
124
106
129