A randomized experiment is a study where subjects are randomly assigned to treatment groups, which balances out lurking variables and lets you draw cause-and-effect conclusions. In AP Stats Topic 9.2, it's one of the two data-collection methods (along with a random sample) that satisfies the independence condition.
A randomized experiment is a study design where the researcher actively imposes treatments on subjects and uses chance (like a random number generator or drawing names) to decide who gets which treatment. That random assignment is the whole point. It spreads lurking variables roughly evenly across the groups, so if the treatment groups end up different, you can credit the treatment itself rather than some hidden confounding variable.
In Unit 9, randomized experiments show up in a specific job. When you build a confidence interval for the slope of a regression line, one of the conditions you must check is independence, and the CED says data should be collected using either a random sample or a randomized experiment. Random assignment also makes the slope estimate b more trustworthy, because confounding variables can't quietly bend the relationship between x and y. In short, the experiment design you learned earlier in the course is what earns you the right to do slope inference later.
This term lives in Topic 9.2, Confidence Intervals for the Slope of a Regression Model, supporting learning objective 9.2.B (verify the conditions to calculate confidence intervals for the slope). The essential knowledge spells it out. To check independence, data should come from a random sample or a randomized experiment. If you skip this check in an FRQ, you lose credit even if your interval math is perfect. The deeper payoff is about scope of conclusions. A randomized experiment is the only design that lets you say the explanatory variable causes changes in the response, which is exactly the kind of conclusion question AP loves to ask after you've computed an interval for the slope β.
Keep studying AP Statistics Unit 9
Random Assignment (Unit 9)
Random assignment is the engine inside a randomized experiment. The experiment is the overall design, while random assignment is the specific act of using chance to sort subjects into treatment groups. One Fiveable-style question describes a researcher randomly assigning 60 students to new tutoring or traditional instruction, and 'randomized experiment' is the term that names that whole setup.
Random Sample (Unit 9)
These are the two doors into the independence condition for slope inference. A random sample tells you who gets studied; random assignment in an experiment tells you who gets which treatment. The CED accepts either one as evidence that observations are independent in Topic 9.2.
Confidence Interval (Unit 9)
A randomized experiment is what makes a confidence interval for the slope, b ± t*(SEb), actually mean something. The interval estimates the true slope β, and the experimental design is what lets you interpret that slope causally instead of just as an association.
Control Group (Unit 9)
Most randomized experiments include a control group (often a placebo group) so the treatment has a baseline for comparison. The 2023 FRQ about omega-3 supplements versus a placebo is a classic example of this structure on the real exam.
Expect randomized experiments in two flavors. First, condition-checking questions in Unit 9 inference. Multiple-choice stems ask things like which scenario violates the independence condition for regression analysis, and the right reasoning hinges on whether data came from a random sample or randomized experiment. Second, design-and-conclusion FRQs. The 2023 FRQ on fiber-reinforced concrete and the 2023 FRQ comparing an omega-3 supplement to a placebo both center on experimental design, and the 2018 ACL recovery question tests whether a causal conclusion is justified. On FRQs, you need to do three things with this term. Verify the condition explicitly when running slope inference, explain why random assignment controls for confounding variables, and match your conclusion to the design (causation is only on the table if treatments were randomly assigned).
A random sample is about selection. You randomly choose which individuals from the population end up in your study, which lets you generalize results to that population. A randomized experiment is about assignment. You randomly decide which treatment each subject receives, which lets you conclude cause and effect. They answer different questions. Random sampling earns generalization, random assignment earns causation, and a study can have one, both, or neither. For the Topic 9.2 independence condition, either one works.
A randomized experiment uses chance to assign subjects to treatment groups, which balances lurking variables and supports cause-and-effect conclusions.
In Topic 9.2, the independence condition for a slope confidence interval is satisfied when data come from a random sample or a randomized experiment.
Random assignment is what separates an experiment from an observational study, and only experiments justify causal claims about the slope.
Random sampling lets you generalize to a population, while random assignment in an experiment lets you claim causation. Don't swap them.
On FRQs, explicitly state that the data came from a randomized experiment when checking conditions, or you can lose credit even with correct calculations.
It's a study where the researcher randomly assigns subjects to treatment groups, like randomly splitting 60 students between a new tutoring method and traditional instruction. Random assignment balances out confounding variables so observed differences can be attributed to the treatment.
Yes, it's the only study design that supports cause-and-effect conclusions in AP Stats. Random assignment spreads lurking variables evenly across groups, so the treatment is the only systematic difference between them.
A random sample randomly selects who is in the study, which lets you generalize to the population. A randomized experiment randomly assigns treatments, which lets you conclude causation. For the independence condition in Topic 9.2, either one counts.
Learning objective 9.2.B requires you to verify conditions before building the interval b ± t*(SEb), and the independence check requires data from a random sample or a randomized experiment. The design also keeps confounding variables from distorting the slope estimate.
You need at least two treatments to compare, and one of them is often a control or placebo group, like the placebo group in the 2023 omega-3 FRQ. What makes it a randomized experiment is random assignment to those groups, not the control group itself.