Sample

Definition

A sample is a subset of a larger population that is selected and studied to gain insights about the entire population. It is a fundamental concept in statistics and probability, as it allows researchers to make inferences about the characteristics of a population without having to study the entire population.

5 Must Know Facts For Your Next Test

1. Samples are used to make inferences about the characteristics of a population, such as the mean, proportion, or distribution of a variable.
2. The quality of a sample is determined by its representativeness, which is influenced by the sampling method used and the size of the sample.
3. Larger samples generally provide more reliable estimates of population parameters and reduce the impact of sampling error.
4. Random sampling is a common technique that ensures each member of the population has an equal chance of being selected, reducing the risk of bias.
5. Samples can be used to estimate population parameters, test hypotheses, and make predictions about the behavior of the larger population.

Review Questions

• Explain how a sample is used to make inferences about a population.
  • A sample is a subset of a larger population that is selected and studied to gain insights about the entire population. By analyzing the characteristics of the sample, such as the mean, proportion, or distribution of a variable, researchers can make inferences about the corresponding population parameters. This allows them to draw conclusions about the population without having to study the entire group, which is often impractical or impossible.
• Describe the factors that influence the quality and representativeness of a sample.
  • The quality and representativeness of a sample are influenced by the sampling method used and the size of the sample. Random sampling, where each member of the population has an equal chance of being selected, helps ensure the sample is representative of the population. Larger samples generally provide more reliable estimates of population parameters and reduce the impact of sampling error, which is the difference between a sample statistic and the true population parameter.
• Analyze the role of samples in statistical inference and hypothesis testing.
  • Samples play a crucial role in statistical inference and hypothesis testing. By studying the characteristics of a sample, researchers can make inferences about the population and test hypotheses about population parameters. Samples allow researchers to estimate population parameters, such as the mean or proportion, and determine the likelihood of observed sample statistics occurring under a given null hypothesis. This enables researchers to draw conclusions about the population and make informed decisions based on the available data, without having to study the entire population.

Related terms

Population:

The entire group or set of individuals, objects, or measurements that are of interest for a particular study or investigation.

Sampling: The process of selecting a representative subset (sample) from a larger population to study and draw conclusions about the population.

Sampling Error:

The difference between a sample statistic and the true population parameter, which can occur due to the natural variability in the data or the way the sample was selected.