AP Statistics Practice Quiz: Introduction to Planning a Study

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

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

In the context of a statistical study, what is the term for the entire group of items or subjects of interest?

A)A sampleB)A populationC)A treatmentD)An experimental unit

All Questions (16)

In the context of a statistical study, what is the term for the entire group of items or subjects of interest?

A) A sample

B) A population

C) A treatment

D) An experimental unit

Correct Answer: B

According to the provided content, a population consists of all items or subjects of interest.

A researcher surveys 200 randomly selected students from a university to understand their opinions on campus dining. This group of 200 students is best described as what?

A) A population

B) An experiment

C) A treatment

D) A sample

Correct Answer: D

The provided content defines a sample as a subset of the population. The 200 students are a subset of the entire university population.

A scientist wants to study the relationship between air pollution levels and the prevalence of asthma in different cities. The scientist gathers data on air quality and asthma rates from 50 cities without altering any conditions. What type of study is this?

A) An experiment

B) An observational study

C) A population study

D) A causal study

Correct Answer: B

This is an observational study because the investigator is simply observing and collecting data. No treatments (like changing air pollution levels) are being imposed.

To test a new type of plant food, a gardener takes 30 identical rose bushes. Fifteen bushes are randomly chosen to receive the new food, while the other fifteen receive standard food. The number of blooms on each bush is counted after one month. This study design is an example of:

A) An observational study

B) A sample survey

C) An experiment

D) A population analysis

Correct Answer: C

This is an experiment because different conditions (treatments, in this case, the types of plant food) are assigned to the experimental units (the rose bushes).

What is the fundamental characteristic that distinguishes an experiment from an observational study?

A) Experiments always use larger samples than observational studies.

B) In an experiment, treatments are assigned to subjects, whereas in an observational study, they are not.

C) Observational studies can only be generalized to the sample, while experiments can be generalized to the population.

D) Experiments involve collecting quantitative data, while observational studies involve qualitative data.

Correct Answer: B

The provided content states that in an experiment, treatments are assigned, while in an observational study, treatments are not imposed. This is the key difference.

A study of a city's residents found that people who own a pet tend to have lower blood pressure than people who do not. The study did not assign pets to people. Why is it inappropriate to conclude that owning a pet causes lower blood pressure?

A) The sample size was likely too small.

B) The study was an observational study, from which causal relationships cannot be determined.

C) The population of the city is not representative of the entire country.

D) Blood pressure is not a valid subject for a statistical study.

Correct Answer: B

Because this is an observational study (treatments were not imposed), it can only show an association. The content explicitly states that causal relationships cannot be determined from an observational study.

A television news station asks its viewers to vote online to express their opinion on a proposed local law. Over 10,000 people vote. Why are the results of this poll not generalizable to the entire population of the city?

A) The sample was not randomly selected and is therefore not likely to be representative of the population.

B) The study was an experiment, and experiments cannot be generalized.

C) The sample size of 10,000 is too small to represent a city.

D) Causal relationships cannot be determined from this type of poll.

Correct Answer: A

The sample consists of people who chose to vote, not a randomly selected or representative sample of the city. The content states that generalizations about a population can only be made from such samples.

A researcher at a hospital in Chicago randomly selects 300 patient records and finds that patients who were visited by a therapy dog had shorter hospital stays on average than patients who were not. To which population can this finding be generalized?

A) All hospital patients in the world.

B) All hospital patients in the United States.

C) All patients at that specific hospital in Chicago.

D) Only the 300 patients included in the sample.

Correct Answer: C

According to the content, a sample is only generalizable to the population from which it was selected. Since the sample was randomly selected from a specific hospital, the results can be generalized to all patients of that hospital.

For the results of a sample survey to be reliably generalized to the population from which the sample was drawn, what is the most important condition?

A) The sample must be a large fraction of the population.

B) The study must be an experiment.

C) The sample must be randomly selected or otherwise representative of the population.

D) The survey questions must not be personal.

Correct Answer: C

The provided content explicitly states that generalizations about a population can only be made from randomly selected or representative samples.

A researcher wants to test if a new drug reduces anxiety. The researcher recruits volunteers through an online ad. Half of the volunteers are randomly assigned the new drug, and the other half are assigned a placebo. The drug is found to significantly reduce anxiety in the treatment group. What is the most appropriate conclusion?

A) The drug causes a reduction in anxiety, and this result applies to everyone with anxiety.

B) There is an association, but not a causal link, between the drug and anxiety reduction.

C) The drug appears to cause a reduction in anxiety for a group like the volunteers, but the result may not be generalizable to the entire population of people with anxiety.

D) No conclusion can be drawn because this is an observational study.

Correct Answer: C

Because treatments were randomly assigned, it is an experiment, and a causal conclusion can be suggested. However, the sample was made of volunteers, not a random sample from the population of interest. Therefore, according to the content, the results are not generalizable to the broader population.

A researcher compares the academic performance of students who play a musical instrument with those who do not. The researcher gathers data from school records and finds that the students who play an instrument have higher average grades. What type of study is this, and what is its primary limitation?

A) Experiment; it cannot be generalized to all students.

B) Observational study; it cannot establish that playing an instrument causes higher grades.

C) Experiment; it cannot establish a causal relationship.

D) Observational study; the sample size is too small to draw conclusions.

Correct Answer: B

This is an observational study because the researcher did not assign students to play an instrument; they simply observed pre-existing groups. The primary limitation of such a study is that it cannot determine causation.

A well-conducted observational study based on a random sample of a population can provide what kind of conclusion?

A) A conclusion about a causal relationship that is generalizable to the population.

B) A conclusion about an association that is generalizable to the population.

C) A conclusion about a causal relationship for the sample only.

D) No valid conclusions can be made from an observational study.

Correct Answer: B

Because the study is observational, it cannot determine causation. However, because the sample is random, its findings (of an association) can be generalized to the population from which the sample was drawn.

A school district wants to know if a new online math program causes an increase in test scores and wants the findings to apply to all 10,000 students in the district. Which study design is most appropriate?

A) Offer the program to all students and compare the district's average test score to the previous year's average.

B) Randomly select 500 students from the district and randomly assign 250 to use the program and 250 to use the traditional method.

C) Ask for 500 student volunteers and allow them to choose whether to use the new program or the traditional method.

D) Randomly select 500 students and observe which ones use the online program, then compare their scores to those who do not.

Correct Answer: B

To establish causation ('causes an increase'), an experiment with random assignment of treatments is necessary. To ensure the findings apply to all students ('generalizable'), a random sample from the population of interest is required. This option includes both random selection and random assignment.

Which of the following describes a study where investigators do not impose treatments but simply observe and measure variables of interest?

A) An experiment

B) An observational study

C) A random sample

D) A population

Correct Answer: B

This is the definition of an observational study as provided in the content.

A sample of subjects is selected from a population. This sample is only useful for making generalizations about which group?

A) Any population with similar characteristics.

B) The population from which it was selected.

C) Only the sample itself.

D) Any population, as long as the sample is large enough.

Correct Answer: B

The provided content explicitly states that a sample is only generalizable to the population from which it was selected.

If a study's goal is to determine if one variable causes a change in another variable, which type of study should be designed?

A) An observational study, because it does not interfere with the subjects.

B) A survey, because it can gather opinions from a large number of people.

C) An experiment, because different conditions (treatments) can be assigned to determine their effect.

D) An observational study, as long as the sample is randomly selected.

Correct Answer: C

The content specifies that causal relationships cannot be determined from an observational study. An experiment, where treatments are assigned, is the appropriate design for investigating causation.