annals of the university of petroşani ∼ economics ∼ vol. xi - part i ...

The Use of Ranking Sampling Method within Marketing Research 85
1500
I = (14360 ± 2 ⋅ ) = (14360 ± 500) =(13860; 14860) (lei)
36
As a consequence, the turnover falls between 13860 and 14860 lei per month,
with a probability of 95.44%. This precision provided by the pilot-sample is not
satisfactory for the managers of the company,
because the error of the turnover
z s
α
estimation ( E = ⋅
= 500 lei) is four times greater than desired.
n
The sample size, which might ensure an estimation limit error of 120 lei results
from:
2 2
⎛ z⋅s⎞ ⎛ 2⋅1500⎞
n = ⎜ ⎟ = ⎜ ⎟ = 625
E 120
⎝
⎠ ⎝ ⎠
(enterprises)
If the permissible limit error was of 60 de lei, the sample would be of size:
⎛
⎝
⎞
⎠
2
2⋅1500
n = ⎜ ⎟ = 2500 (enterprises)
60
Therefore, improving estimation accuracy by reducing by half the admissible
limit error requires increasing by four times the number of companies taken in the
sample.
The volume of the proportional sample is calculated using the same formula:
2 2 n
⎛ z⋅
s⎞ z ⎛ 2 ⎞
i i
n = ⎜ ⎟ = ⎜∑ k ⋅s
⎟
(14)
E E =
⎝
⎠
⎝
k 1
2
2
n = ( 0,17 ⋅ 1000 )
2 + 0, 50 ⋅ 1500 2 + 0, 33 ⋅ 1700
2
=
2
120
= 624, 63 ≈ 625 (enterprises)
The sample size that provides an estimation of the monthly turnover average
with a maximum permissible error of 120 lei and a confidence level of 95.44% is of
625 enterprises, and it is equal to the unstratified sample. However, the elements of the
sample will be selected in a way that the structure of the general collectivity should be
reproduced exactly. The size of each stratum results from the relationship:
n = k ⋅ n
i
n 1 =0,17 x 625 ≈ 106 (enterprises)
n 2 =0,50 x 625 ≈ 313 (enterprises)
n 3 =0,33 x 625 ≈ 206 (enterprises)
i
⎠