Question 1

A researcher wants to determine if a new teaching method improves student test scores. She randomly selects 100 students from a school and randomly assigns half to the new method and half to the traditional method. After the semester, she compares their scores. Which of the following conclusions is justified based on the study design?

Accepted Answer

The new teaching method causes higher test scores for all students at the school.

Question 2

Which of the following best describes the role of random assignment in an experiment?

Accepted Answer

It allows us to establish a causal relationship between variables.

Question 3

A study finds that students who took an SAT prep course scored higher on average than those who did not. The study surveyed all students in a senior-only class and divided them based on whether they took the course. Which conclusion is most appropriate?

Accepted Answer

For the students in this class, there is an association between taking an SAT prep course and higher SAT scores.

Question 4

In which scenario can you both generalize to the population and infer causation?

Accepted Answer

When individuals are randomly selected and randomly assigned to groups.

Question 5

Zach conducts a study on iPhones by randomly selecting 20 new phones from his store and randomly assigning them to low or high screen brightness groups. He measures battery life for each phone. What type of study is this?

Accepted Answer

An experiment, because there was random assignment to treatments.

Question 6

Which of the following is the explanatory variable in Zach's iPhone battery study?

Accepted Answer

Screen brightness (low or high)

Question 7

A researcher selects a random sample of seniors from a school and asks whether they took an SAT prep course, then compares their SAT scores. Which inference is justified?

Accepted Answer

There is an association between taking an SAT prep course and higher SAT scores for all seniors at the school.

Question 8

Which of the following best describes the response variable in an experiment?

Accepted Answer

The variable that is measured as the outcome of the study.

Question 9

Suppose a study randomly assigns half of a random sample of seniors to take an SAT prep course and the other half not to. Both groups take the SAT. What can be concluded?

Accepted Answer

Taking an SAT prep course causes higher SAT scores for all seniors at the school.

Question 10

Which of the following is true about random sampling?

Accepted Answer

It allows us to generalize results to the population from which the sample was drawn.

Question 11

A study selects a random sample of students who have taken the SAT and randomly assigns half to take a prep course. What is the scope of inference?

Accepted Answer

We can generalize to all students who have taken the SAT at the school and infer causation.

Question 12

Which of the following best describes the difference between random sampling and random assignment?

Accepted Answer

Random sampling allows generalization to the population; random assignment allows inference of causation.

Question 13

A study divides all students in a senior-only class based on whether they took an SAT prep course and compares their SAT scores. What type of study is this?

Accepted Answer

Observational study

Question 14

If a study uses random assignment but not random sampling, what can be inferred?

Accepted Answer

Causation for the sample studied, but not generalization to the population.

Question 15

Which of the following is a necessary condition to infer that a treatment causes a change in the response variable?

Accepted Answer

Random assignment to treatment groups

Question 16

A study finds a significant association between two variables but did not use random assignment. What can be concluded?

Accepted Answer

There is an association, but causation cannot be inferred.

Scope of Inference: Random Sampling and Random Assignment in Statistical Studies

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