Research Methodology - Dr. Krishan K. Pandey

178 Research Methodology
2 2
p
z σ
n =
2
e
b g b g
b g
2 2
= = = 257 . 2 26. 4196
4128 . ~ − 41
2
08 . 064 .
Thus, in the given case the sample size remains the same even if we assume infinite population.
In the above illustration, the standard deviation of the population was given, but in many cases
the standard deviation of the population is not available. Since we have not yet taken the sample and
are in the stage of deciding how large to make it (sample), we cannot estimate the populaion standard
deviation. In such a situation, if we have an idea about the range (i.e., the difference between the
highest and lowest values) of the population, we can use that to get a crude estimate of the standard
deviation of the population for geting a working idea of the required sample size. We can get the said
estimate of standard deviation as follows:
Since 99.7 per cent of the area under normal curve lies within the range of ± 3 standard deviations,
we may say that these limits include almost all of the distribution. Accordingly, we can say that the
given range equals 6 standard deviations because of ± 3. Thus, a rough estimate of the population
standard deviation would be:
6 $σ = the given range
or $σ
the given range
=
6
If the range happens to be, say Rs 12, then
$σ=
12
=
6
Rs 2.
and this estimate of standard deviation, $σ , can be used to determine the sample size in the formulae
stated above.
(b) Sample size when estimating a percentage or proportion: If we are to find the sample size for
estimating a proportion, our reasoning remains similar to what we have said in the context of estimating
the mean. First of all, we shall have to specify the precision and the confidence level and then we will
work out the sample size as under:
Since the confidence interval for universe proportion, $p is given by
p ⋅ q
p ± z⋅
n
where p = sample proportion, q = 1 – p;
z = the value of the standard variate at a given confidence level and to be worked out from
table showing area under Normal Curve;
n = size of sample.