Sample without replacement

Definition

Sampling without replacement refers to the method of selecting items from a population where each item can only be selected once. This means that after an item is chosen, it is not returned to the pool for potential selection again. This technique is significant as it influences the probabilities associated with subsequent selections and is essential when constructing confidence intervals for a population proportion.

5 Must Know Facts For Your Next Test

1. When sampling without replacement, the selection of each sample affects the probabilities for the remaining selections, making this method useful for small populations.
2. The sample size plays a crucial role; if it exceeds 10% of the population size, adjustments must be made to the standard error to account for the lack of replacement.
3. In constructing confidence intervals for a population proportion, using samples without replacement allows for more accurate estimates as it reduces variability in the sample proportions.
4. This sampling method is particularly important in survey research, where it ensures that the same respondent does not provide multiple responses, leading to biased results.
5. When calculating probabilities related to samples taken without replacement, hypergeometric distributions are often used instead of binomial distributions.

Review Questions

• How does sampling without replacement impact the accuracy of estimating a population proportion?
  • Sampling without replacement helps improve accuracy in estimating a population proportion because it ensures that each selected individual is unique and not counted multiple times. This leads to reduced variability in the sample proportion and allows researchers to construct more reliable confidence intervals. By considering only distinct individuals, researchers can better reflect the true characteristics of the entire population.
• Discuss how sampling without replacement affects the calculation of standard errors when constructing confidence intervals.
  • When constructing confidence intervals, using samples without replacement means that the standard error must be adjusted, especially if the sample size is large relative to the population size. The finite population correction factor is applied to account for this lack of replacement, which leads to a smaller standard error than would be calculated using simple random sampling with replacement. This adjustment is crucial for obtaining valid confidence intervals.
• Evaluate the implications of using sampling without replacement in survey research and its influence on data integrity.
  • Using sampling without replacement in survey research significantly enhances data integrity by preventing duplicate responses from individuals. This practice ensures that each participant's input reflects their individual opinion rather than skewing results through repeated sampling. Consequently, this method fosters more accurate representation of the target population and enhances the reliability of findings, allowing for informed decision-making based on the survey data.

Related terms

Population:

The entire group of individuals or items that researchers are interested in studying.

Sampling Distribution:

The probability distribution of all possible sample proportions that can be obtained from a population.

Confidence Interval:

A range of values used to estimate the true parameter of a population, typically expressed at a certain confidence level.