Question

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. \(\dfrac{N-n}{N-1}\)

Answer 1

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 X₁, X₂, ..., X_n, 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