Every statistical study starts with an investigative question about a population, and the question decides how the data should be collected. A survey of a sample describes a population; only an experiment, where the researcher assigns treatments, can show cause and effect. Sort the questions and studies below, then watch a hidden variable fake a cause.
Three hands-on parts. Your score updates as you go.
A statistical investigative question asks about a population and expects the answer to depend on data that vary. A question with one fixed answer, or about one individual, is not statistical.
Census: data from every member of the population. Sample survey: data from a sample to describe a population. Observational study: researchers observe and measure without assigning treatments. Experiment: researchers impose treatments and observe the response.
This simulated observational study follows 400 adults. In this world, coffee has no effect on heart problems unless you add one with the slider. Smoking does raise the risk, and smokers are also more likely to drink coffee.
A good investigative question names the population and the variable and anticipates variability: "How many hours do students at our school typically sleep on school nights?"
The population is the entire group the question is about. A sample is the part of the population we actually collect data from. A census collects data from everyone.
A parameter describes a population (usually unknown). A statistic describes a sample and is used to estimate the parameter. Memory trick: population–parameter, sample–statistic.
If the researcher assigns the treatment, it is an experiment. If subjects choose or already have the condition, it is observational, even when it uses fancy equipment or a lab.
A confounding variable is related to the explanatory variable and also affects the response, so their effects cannot be separated. Smoking confounds coffee and heart problems in Part C.
An observational study can show an association, but not that one variable causes the other. A well-designed experiment with random assignment can.
The question you ask decides how you should collect data.
| Investigative question | Method | What you can conclude |
|---|---|---|
| What proportion of all 1,200 students at our school have a part-time job? | Sample survey (random sample), or a census if feasible | An estimate of the proportion for all students at the school |
| Does a new study app improve vocabulary quiz scores? | Experiment: randomly assign students to use the app or not | Whether the app causes higher scores, for subjects like these |
| Do students who play varsity sports have higher GPAs? | Observational study (you cannot assign sports) | Association only; motivation or time management could confound |
| What is the average age of the 28 people on our soccer team? | Census of the team | The exact parameter; no estimate needed |
| Is it 72°F outside right now? | Not a statistical question | One fixed answer; no variability to study |
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 1.10. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 1 terminology guide.