Researchers rely on what to draw meaningful conclusions from collected data?

Researchers rely on probability theory to draw meaningful conclusions from collected data because it provides the foundational framework for making inferences, estimating parameters, and assessing the reliability of outcomes based on sample data. Probability theory allows for the quantification of uncertainty and the formulation of hypotheses. By utilizing this theory, researchers can determine the likelihood of observing certain data patterns or results if a particular hypothesis were true, helping them to make logical conclusions that are supported by statistical evidence.

In the context of statistical analysis, probability theory underpins many statistical techniques, including regression analysis, hypothesis testing, and confidence intervals. These tools are essential for interpreting results from experiments or observational studies in a way that incorporates randomness and variation inherent to real-world data.

While empirical distribution deals with data as it is observed and can help in understanding data patterns, it does not provide the theoretical framework that probability theory offers. The central limit theorem is certainly important for understanding the distribution of sample means, particularly as sample size increases, but it is a specific result stemming from probability theory rather than the overarching framework used for general inference. Theoretical distributions describe idealized probability distributions such as normal or binomial distributions, which represent how variables behave under certain assumptions, but they rely on the concepts and principles derived from probability theory.