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n=

Where,

n = Size of Sample

z = z score associated with level of confidence

p = sample proportion

e = margin of error

ii. Cochran’s formula

Cochran’s formula is a powerful tool used in statistical research
to determine the appropriate sample size for a given study or
experiment. Developed by William G. Cochran, a prominent
statistician, the formula takes into account factors such as the
desired level of confidence, margin of error, and the population
size to provide an optimal sample size estimation.

a. Cochran’s formula for calculating sample size when the
population is infinite

Cochran (1977) developed a formula to calculate a representative
sample for proportions as:
n
0 =

where,

n = sample size
0
z = selected critical value of desired confidence level

p = estimated proportion of the population

q = 1-p
e = desired level of precision

For example, in a city, a study has to be undertaken to determine
the proportion of people who support a particular political candidate
during election. Determine the sample size needed for a 95 percent
confidence level with a margin of error of 5 percent. Based on past
data, the proportion of people supporting the candidate is assumed
to be around 0.5.

74 SGOU - SLM -MCom Research Methodology