Question

Please use examples to explain the principle on how to calculate the sample size.

Answer 1

Cochran's formula is employed to calculate the sample size given a desired level of precision, desired confidence level and estimated proportion of the attribute present in the population.

The Cochran's formula is given by:

$n_{0}=\frac{Z^{2}\times p\times q}{e^{2}}$

where

Z is obtained from the Z Table corresponding to the given Significance level $\alpha$

p is the estimated proportion of the population which has the attribute in question

q = 1- p

e is the desired level of precision (Margin of Error)

Example:

Suppose the researcher wants to estimate how many households make breakfast in the morning. Since he does not have any information, he assumes = 0.5. Suppose he wants 95% confidence and $\pm$ 5% precision.

A 95% confidence level gives 1.96 as per Normal Table.

Substituting the values, we get:

$n_{0}=\frac{1.96^{2}\times 0.5\times (1-0.5)}{0.05^{2}}=385$

Thus, we get Sample Size = 385.