Page 155 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Quantitative Techniques-II

Notes
n 200
n =  N   1,000
3
3 N 10,000
= 20

n 200
n =  N   500
4
4 N 10,000
= 10

n
n =  N  10
5
5 N
n = n + n + n + n + n
1 2 3 4 5
= 120 + 40 + 20 + 10 + 10
= 200

Sample Disproportion

Let is the variance of the stratum i,

where i = 1,2,3……….k.
The formula to compute the sample size of the stratum i is the variance of the stratum i,
where size of stratum i
r = Sample size of stratum i
i

r =
i
r = Ratio of the size of the stratum I with that of the population.
i
N = Population of stratum i
i
N = Total population.

Example: The Government of India wants to study the performance of women self help
groups (WSHGs) in three regions viz. North, South and West. The total number of WSHGs is
1,500. The number of groups in North, South and West are 600, 500 and 400 respectively. The
Government found more variation between WSHGs in the North, South and West regions. The
variance of performance of WSHGs in these regions are 64, 25 and 16 respectively. If the
disappropriate stratified sampling is to be used with the sample size of 100, determine the
number of sampling units for each region.

Solutions:
Total Population N = 1,500
Size of the stratum 1, N = 600
1
Size of the stratum 2, N = 500
2
Size of the stratum 3, N = 400
3
Variance of stratum 1,  = 12 = 64

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