key term - Sample Statistic

Definition

A sample statistic is a numerical value calculated from a sample of data that is used to estimate or describe a characteristic of the larger population from which the sample was drawn. It serves as a representation of the population parameter and is a key component in the process of statistical inference.

5 Must Know Facts For Your Next Test

1. Sample statistics are used to estimate population parameters, such as the mean, proportion, or standard deviation.
2. The accuracy of a sample statistic as an estimate of a population parameter depends on the size and representativeness of the sample.
3. Sample statistics are subject to sampling variability, meaning that different samples drawn from the same population will generally yield different sample statistics.
4. The sampling distribution of a sample statistic, such as the sample mean or sample proportion, can be used to quantify the uncertainty associated with using the sample statistic to estimate the corresponding population parameter.
5. The central limit theorem is a fundamental concept in statistics that describes the sampling distribution of the sample mean, which is approximately normal for large sample sizes.

Review Questions

• Explain the role of sample statistics in the context of a sampling experiment.
  • In a sampling experiment, sample statistics are used to estimate or describe characteristics of the larger population from which the sample was drawn. The sample statistic serves as a representation of the unknown population parameter, and the accuracy of this estimate depends on the size and representativeness of the sample. By understanding the sampling distribution of the sample statistic, researchers can quantify the uncertainty associated with using the sample statistic to draw inferences about the population.
• Describe how the central limit theorem relates to the sampling distribution of the sample mean.
  • The central limit theorem is a fundamental concept in statistics that states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution, as long as the sample size is sufficiently large. This property of the sample mean's sampling distribution is crucial for making inferences about the population mean, as it allows researchers to use the normal distribution to quantify the uncertainty associated with using the sample mean as an estimate of the population mean.
• Analyze how the size and representativeness of a sample can impact the accuracy of a sample statistic as an estimate of a population parameter.
  • The size and representativeness of a sample are key factors that determine the accuracy of a sample statistic as an estimate of a population parameter. Larger sample sizes generally result in sample statistics that are more representative of the population, as they reduce the impact of sampling variability. Additionally, if the sample is not representative of the population, the sample statistic may be biased and fail to accurately estimate the corresponding population parameter. Researchers must carefully design their sampling procedures to ensure that the sample is both large enough and representative of the population in order to draw valid inferences from the sample data.

Related terms

Population Parameter:

A numerical value that describes a characteristic of the entire population, such as the mean or standard deviation, which is unknown and must be estimated using sample data.

Sampling Experiment:

The process of selecting a subset (sample) of individuals from a population to study and make inferences about the larger population.

Sampling Distribution:

The probability distribution of a sample statistic, which describes how the statistic would vary if the sampling experiment was repeated many times.