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AP Statistics Practice Quiz: Inference and Experiments

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 11 questions to check your progress.

Question 1 of 11

According to the principles of statistical inference, what is the primary goal when drawing conclusions from data?

All Questions (11)

According to the principles of statistical inference, what is the primary goal when drawing conclusions from data?

A) To prove a hypothesis with absolute certainty.

B) To attribute the conclusions to the broader distribution from which the data were collected.

C) To describe the characteristics of the specific data sample collected.

D) To eliminate all possible sources of bias in data collection.

Correct Answer: B

Based on the provided content, 'Statistical inference attributes conclusions based on data to the distribution from which it was collected.' This is its core purpose, extending findings beyond the immediate sample.

In a well-designed experiment, what is the main benefit of using random assignment of treatments to experimental units?

A) It ensures that the experimental units are representative of a larger population.

B) It guarantees that the results of the experiment will be statistically significant.

C) It allows for the conclusion that observed changes are unlikely to be due to chance.

D) It eliminates the need for a control group in the experiment.

Correct Answer: C

The provided content states, 'Random assignment allows concluding that observed changes are unlikely to be due to chance, i.e., are statistically significant.' Its purpose is to create comparable groups to isolate the effect of the treatment from random variation.

An experiment was conducted to test a new fertilizer. Two groups of plants were randomly assigned to either receive the new fertilizer or a standard fertilizer. The group with the new fertilizer showed significantly greater growth. What is the most appropriate conclusion?

A) The new fertilizer is better, and this result can be generalized to all plants.

B) There is evidence that the new fertilizer caused the increased growth in the experimental plants.

C) The difference in growth was likely due to random chance.

D) The experiment was flawed because it did not use a random sample of plants.

Correct Answer: B

The content states that 'Statistically significant differences between treatment groups are evidence that the treatments caused the effect.' Since treatments were randomly assigned and the result was significant, a causal conclusion is warranted for the units in the experiment.

Under which condition can the results of a well-designed experiment be generalized to a larger group?

A) When the results are statistically significant.

B) When the treatments have been randomly assigned to the experimental units.

C) When the experimental units are representative of the larger group.

D) When the sample size of the experiment is very large.

Correct Answer: C

The content explicitly states, 'If experimental units are representative of a larger group, results can be generalized to that group.' While other factors are important for different aspects of inference, representativeness is the key to generalization.

Researchers tested a new teaching method by randomly assigning 100 student volunteers from a single university to either the new method or a traditional one. The students using the new method showed statistically significant improvements in test scores. What is the most accurate conclusion that can be drawn?

A) The new teaching method causes improved test scores for all students everywhere.

B) The new teaching method is associated with, but does not cause, higher scores for all students.

C) For students similar to the volunteers, there is evidence that the new teaching method causes improved test scores.

D) No conclusion can be drawn because the students were volunteers and not randomly selected.

Correct Answer: C

Random assignment allows for a causal conclusion. However, because the sample consists of volunteers from a single university, they are not representative of all students. Therefore, the causal conclusion can only be generalized to a group similar to the experimental units.

When the results of an experiment are described as 'statistically significant,' what does this imply?

A) The results are of great practical importance.

B) The observed effect is too large to be reasonably attributed to chance.

C) The experiment was conducted without any errors or bias.

D) The results can be generalized to the entire population.

Correct Answer: B

The content explains that random assignment allows us to conclude that observed changes are 'unlikely to be due to chance, i.e., are statistically significant.' This means the effect is likely real and not just a random fluke.

A study finds that people who drink coffee daily have a lower incidence of a certain disease than people who do not. The difference is statistically significant. Why is it inappropriate to conclude that drinking coffee *causes* a reduced risk of the disease?

A) The result was not statistically significant enough to claim causation.

B) The study participants were not representative of the general population.

C) Without random assignment to coffee-drinking and non-coffee-drinking groups, we cannot rule out other factors causing the effect.

D) The sample size was likely too small to make a causal claim.

Correct Answer: C

This describes an observational study, not an experiment. The provided content establishes that random assignment is necessary to create treatment groups where statistically significant differences can be attributed to the treatment (causation). Without it, confounding variables could be the real cause of the observed difference.

A pharmaceutical company develops a new headache medication. They recruit 200 volunteers who suffer from chronic headaches and randomly assign half to receive the new medication and half to receive a placebo. The group taking the new medication reports a statistically significant reduction in headache frequency. What is the strongest, most appropriate conclusion?

A) The new medication will reduce headache frequency for everyone.

B) For the volunteers in the study, there is evidence the new medication caused a reduction in headache frequency.

C) There is an association between taking the medication and reduced headaches, but no causal link can be established.

D) The experiment is invalid because the participants were not randomly selected from the population of all headache sufferers.

Correct Answer: B

The use of random assignment allows for a causal conclusion ('caused a reduction'). However, the use of volunteers means the sample is not representative of all headache sufferers, so the results cannot be generalized to everyone. The conclusion is therefore limited to the group studied or those similar to them.

In the context of a well-designed experiment with random assignment, what does a statistically significant difference between treatment groups provide?

A) A guarantee that the results can be generalized.

B) Evidence that the treatments caused the observed effect.

C) Proof that the data was collected from a normal distribution.

D) An indication that the sample was representative of the population.

Correct Answer: B

This is a direct application of the principle from the provided content: 'Statistically significant differences between treatment groups are evidence that the treatments caused the effect.'

A researcher wants to conduct an experiment to prove that a new exercise regimen causes weight loss and to generalize this finding to all adults in a specific city. Which design elements are necessary?

A) Random assignment of the regimen, but the sample does not need to be random.

B) A random sample of adults from the city, but the assignment to the regimen does not need to be random.

C) Both a random sample of adults from the city and random assignment to the exercise regimen.

D) Neither random sampling nor random assignment is required if the results are statistically significant.

Correct Answer: C

To establish causation ('causes weight loss'), random assignment is required. To generalize the findings to all adults in the city, the experimental units must be representative, which is best achieved through a random sample from that population. Both are needed to meet the researcher's goals.

In an experiment, subjects were randomly assigned to two groups to test a new drug. After the trial, the difference in outcomes between the two groups was found to be *not* statistically significant. What is the correct interpretation of this result?

A) The drug has been proven to have no effect whatsoever.

B) The experiment failed to provide convincing evidence that the drug caused an effect.

C) The lack of significance means the random assignment process was flawed.

D) The drug definitely caused the observed difference, but the effect was too small to be important.

Correct Answer: B

A non-significant result means that the observed difference is small enough that it could have reasonably occurred by chance alone. It does not prove there is no effect, but it does mean we lack sufficient evidence to conclude the treatment caused an effect. The experiment did not yield evidence of a causal relationship.