Elementary Statstics

3.1.12.1 Determination of sample size

A number of formulae have been devised for determining the sample size depending upon the availability of information. A few formulae are given below:

where

n= Sample size

Z=Value at a specified level of confidence or desired degree of precision.

= Standard deviation of the population

d = Difference between population mean and sample mean.

The steps in computing the sample from the above formula are:

(i) Select the desired degree of precision, i.e., specified level of confidence and designate it as small ‘z’ (at 1% level of significance or 99% confidence level the value of ‘z’ is 2-58 and at 5% level of significance or 95% confidence level 1.96)

(ii) Multiply the ‘z’ selected in step 1 by the standard deviation of the universe which may be assumed.

(iii) Divide the product of the preceding step by the standard error of mean or difference between population and sample mean. Square the resultant quotient. The result is the size of sample required.

Example. Determine the sample size if $$\sigma=6,$$ population mean=25, Sample means=23 and the desired degree of precision is 99%.

Solution