Back to Exercise: Distinguish surveys, experiments, and observational studies

Exercises: Distinguish Surveys, Experiments, and Observational Studies

Work through each section in order. For classification problems, decide whether a study is a sample survey, an observational study, or a randomized experiment, and use two separate questions: "Was there random SELECTION?" (which governs whether results generalize to a population) and "Was there random ASSIGNMENT?" (which governs whether a difference can be read as causation). For explanation problems, write in complete sentences.

Grade 10·21 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-ic-b-3

Work through problems with immediate feedback

Warm-Up: Study Vocabulary

These problems review the vocabulary you will use throughout.

In a study of an after-school tutoring program, researchers decide who attends tutoring by flipping a coin for each student, then compare the two groups' test scores. What kind of study is this?

A randomized experiment, because the researchers impose the treatment (who attends) by chance.

A sample survey, because students are asked about their scores.

An observational study, because the researchers watch scores without intervening.

None of these, because comparing two groups is not a real study design.

Researchers compare the test scores of students who CHOSE to attend tutoring against students who chose not to. No one was assigned to a group; the researchers only watch the groups that already exist. What kind of study is this?

An observational study, because it compares pre-existing groups without imposing a treatment.

A randomized experiment, because two groups are compared.

A sample survey, because no treatment is imposed.

It is not a study, because the groups were not assigned.

In a tutoring experiment, one group attends tutoring (the treatment group) and the other group does not (the control group). A student says, "The control group gets nothing, so it is a pointless waste of subjects." What is the BEST correction?

The control group is the baseline the treatment is judged against; without it you could not tell whether the treatment, and not something else, caused a change.

The student is right; the control group does nothing useful and could be dropped.

The control group should also receive the treatment so the study is fair.

The control group matters only if it is larger than the treatment group.

Fluency Practice

Classify each study and identify the role of randomization.

A polling company randomly selects 2,000 adults and asks each whether they exercise daily and how they rate their health. Even with a huge sample, which conclusion can this survey support?

It can estimate and generalize a population characteristic and show association, but it cannot establish that exercise causes better health.

It can prove that exercise causes better health, because the sample is large.

It can prove causation only if the sample is at least 5,000 people.

It can conclude nothing at all, because surveys are unreliable.

In the tutoring experiment, students are assigned to attend tutoring or not, and the researchers then record each student's test score. Identify the two variables. The EXPLANATORY variable is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ . The RESPONSE variable is ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .

explanatory variable:

response variable:

A researcher draws a sample at random from the population, then uses chance to place each chosen subject into a treatment group or a control group. Which two randomizations were used?

Both random selection and random assignment.

Random selection only.

Random assignment only.

Neither — choosing a sample is not randomization.

A study randomly draws a sample of adults from a city and surveys their coffee habits and sleep. It does NOT assign anyone to drink coffee. Which randomization did this study use, and what does it license?

Random selection only; results generalize to the city, but the study shows association, not causation.

Random assignment only; the study can establish that coffee affects sleep.

Both randomizations; the study generalizes AND establishes causation.

Neither randomization; the study can conclude nothing.

A drug is tested on 200 volunteers (not a random sample of any population). The volunteers are randomly assigned to the drug or a placebo, and the drug group recovers faster. To whom can this causal result be generalized?

Only as far as the volunteers represent a broader group; random assignment earns causation within these subjects, but without random selection the result does not automatically generalize to everyone.

To the entire population, because the study was randomized.

To no one, because experiments never generalize.

To everyone who is similar in age only, regardless of how subjects were obtained.

An observational study finds that students who eat breakfast have higher grades than students who skip it. Which conclusion is justified?

Eating breakfast is associated with higher grades, but the study cannot establish that breakfast causes higher grades because of possible confounding variables.

Eating breakfast causes higher grades, because the difference is clear.

Grades cause students to eat breakfast.

There is no relationship between breakfast and grades.

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