Which of the following best describes the relationship between a sample and its population?

The correct answer describes the fundamental concept of sampling in statistics. A sample is defined as a subset of individuals or observations that are selected from a larger population. This means that the sample represents a smaller portion of the overall population, allowing researchers to make inferences about the population based on the analysis of the sample.

When conducting research, it is often impractical or impossible to gather data from every member of a population. Therefore, obtaining a representative sample allows for effective analysis and provides insights into the characteristics and behaviors of the entire population. The size of the sample can vary, but it is always smaller than the population from which it is drawn.

In contrast, the other options presented do not accurately reflect the relationship between samples and populations. For instance, the notion that a sample can perfectly represent its population is idealistic and not typically achievable in practice. Also, stating that a sample is always a larger group than the population contradicts the very definition of a sample. Finally, asserting that a sample includes all members of a population is inaccurate since that would mean it is not a sample but the entire population instead. Thus, recognizing that a sample is a smaller portion of a larger population is crucial for understanding the principles of statistical analysis.