# Sample Size Formula

The number of observation in a given sample population is known as Sample size. Since it not possible to survey the whole population. We take sample from the population and then conduct survey or research. Sample size formula helps us find the accurate sample size through the difference between the population and the sample. Sample size is denoted by “*n*” or “*N*”. Here we write it as “*SS*”.

We should know that the sample size that we are taking from the population, will not hold good for the whole sample. We have a level of confidence and margin of error to calculate that the sample size is accurate or not. Confidence level helps describe how sure you are that the results of the survey hold true or accurate.

The sample size for infinite population is given as:

\[\large SS=\frac{Z^{2}p\left(1-p\right)}{C^{2}}\]

The sample size for finite population is:

\[\large New\;SS=\frac{SS}{1+\left(\frac{SS-1}{Pop}\right)}\]

Where,

*SS* = Sample Size.

*Z* = Given *Z* value

*p* = Percentage of population

*C* = Confidence level

*Pop* = Population

**Solved example**

**Question:** Find the Sample size for finite and infinite population, when percentage of 4300 population is 5, confidence level 99 and confidence interval is 0.01?

**Solution:**

*Z* = From the *z*-table, we have the value of confidence level, that is 2.58 by applying given data in the formula:

$SS=\frac{\left(2.58\right)^{2}0.5\left(1-2.58\right)}{0.01^{2}}=474$

Sample size for finite population $=\frac{474}{1+\left(\frac{474-1}{4300}\right)}$

New SS = 250