Investigative question components, censuses, experiments and observational studies

What the exam asks

Formulate or critique an investigative question by identifying its three required components.
Classify a data-collection method as a census, sample survey, prospective observational study, retrospective observational study, or experiment.
Identify experimental components: experimental units (subjects/participants), explanatory variables (factors), levels, treatments, and response variables.
Explain confounding in context by linking a third variable to both the explanatory and response variables.
Justify the scope of inference (generalization to a population vs. cause-and-effect conclusions).

Under the AP Statistics framework, a complete investigative question must clearly communicate three components:

Variable(s) of interest: What specific characteristic is being measured or recorded on each individual, and how it guides data collection.
Parameter and analysis goal: The numerical summary of the population (such as a population mean $\mu$ or population proportion $p$ ) and the goal—either estimation (finding a confidence interval) or testing a claim with a clear direction for the alternative hypothesis (e.g., “greater than”, “less than”, or “differs from”).
Population and type of conclusion: The entire group of individuals of interest and whether the question seeks a descriptive estimate, an association, or a causal link.

Study Type	How Data Are Collected	Key Feature
Census	Attempts to measure every individual in the entire population of interest.	No sampling variability, though often impractical or impossible.
Sample Survey	A type of observational study that collects data from a subset of a population at a single point in time (often via questionnaires).	Measures existing characteristics without disturbing the individuals.
Retrospective Observational Study	Researchers select a sample and look backward in time at historical records or past behaviors.	Observes without imposing treatments; efficient for rare outcomes.
Prospective Observational Study	Researchers select a sample and follow individuals forward in time to record future outcomes.	Observes without imposing treatments; tracks natural development.
Experiment	Researchers deliberately impose treatments on experimental units and measure the response.	Can establish cause-and-effect if treatments are randomly assigned.