# If the random sample size n is drawn without replacement from a finite population of size N, the correction factor for standard error of sample mean w

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If the random sample size n is drawn without replacement from a finite population of size N, the correction factor for standard error of sample mean will be:
1. $\dfrac{N-1}{N-n}$
2. $\sqrt {\frac{{N - 1}}{{N - n}}}$
3. $\sqrt {\frac{{N - n}}{{N - 1}}}$
4. $\dfrac{N-n}{N-1}$

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Correct Answer - Option 3 : $\sqrt {\frac{{N - n}}{{N - 1}}}$

Explanation:

The population correction factor is given by the formula :

$\sqrt {\frac{{N - n}}{{N - 1}}}$

Sample size = In statistics, the sample size is the measure of the number of individual samples used in an experiment for example,  if we are testing 50 samples of people who watch movie in a city, then the sample size is 50.

Sample mean = The sample mean from a group of observations is an estimate of the population mean (μ).

Given a sample of size n, consider n independent random variables X1X2, ..., Xn, each corresponding to one randomly selected observation. Each of these variables has the distribution of the population, with mean(μ)  and standard deviation (σ).

The sample mean = x̄ = ( Σ xi ) / n