Finite Population Correction Factor

Definition

The finite population correction factor is a statistical adjustment used when sampling from a population that is small relative to the total population size. It accounts for the fact that sampling without replacement from a finite population reduces the variability of the sample compared to sampling with replacement from an infinite population.

5 Must Know Facts For Your Next Test

1. The finite population correction factor is applied when the sample size (n) is a substantial proportion of the total population size (N), typically when n/N > 0.05.
2. The finite population correction factor reduces the standard error of the sample proportion compared to the standard error calculated for an infinite population.
3. The formula for the finite population correction factor is $\sqrt{\frac{N-n}{N-1}}$, where N is the population size and n is the sample size.
4. Applying the finite population correction factor results in a smaller standard error and narrower confidence intervals for the population proportion.
5. The finite population correction factor is most relevant when sampling without replacement from a small population, as it accounts for the decreased variability in the sample compared to sampling with replacement.

Review Questions

• Explain the purpose of the finite population correction factor and how it relates to the sample proportion.
  • The finite population correction factor is used to adjust the standard error of the sample proportion when the sample size is a substantial proportion of the total population size. This is necessary because sampling without replacement from a finite population reduces the variability of the sample compared to sampling with replacement from an infinite population. By applying the finite population correction factor, the standard error of the sample proportion is reduced, resulting in narrower confidence intervals and more precise inferences about the true population proportion.
• Describe the relationship between the finite population correction factor and the standard error of the sample proportion.
  • The finite population correction factor is directly related to the standard error of the sample proportion. Specifically, the finite population correction factor is used to multiply the standard error calculated for an infinite population in order to obtain the correct standard error for a finite population. The formula for the finite population correction factor is $\sqrt{\frac{N-n}{N-1}}$, where N is the population size and n is the sample size. Applying this factor reduces the standard error, which in turn affects the width of confidence intervals and the precision of inferences made about the population proportion.
• Analyze the conditions under which the finite population correction factor should be applied and explain its impact on statistical inference.
  • The finite population correction factor should be applied when the sample size (n) is a substantial proportion of the total population size (N), typically when n/N > 0.05. In these cases, sampling without replacement from the finite population reduces the variability of the sample compared to sampling with replacement from an infinite population. Applying the finite population correction factor accounts for this reduced variability, resulting in a smaller standard error for the sample proportion. This, in turn, leads to narrower confidence intervals and more precise inferences about the true population proportion. The finite population correction factor is most relevant when working with small populations where the sample size is a large fraction of the total population.

Related terms

Population Proportion:

The proportion or percentage of a population that exhibits a particular characteristic or attribute.

Sampling Distribution:

The distribution of a statistic (such as the sample mean or sample proportion) across all possible samples that could be drawn from a population.

Standard Error:

A measure of the variability or spread of a sampling distribution, used to quantify the uncertainty in a sample statistic as an estimate of a population parameter.