AP Statistics : Data

Study concepts, example questions & explanations for AP Statistics

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : How To Conduct A Sample Survey

Shawn would like to determine what the most popular television channel is in his town, called Hearne. 

Which of the following would be an appropriate target population for the survey? 

Possible Answers:

Residents of the town whose contact information can be found in the local directory

Students at the local high school 

Purchasers of a television at the local electronics store 

Attendees of a mass at a local Church

Shoppers at the local grocery store

Correct answer:

Residents of the town whose contact information can be found in the local directory

Explanation:

Since Shawn would like to know the most popular television channel in his town, he must include all residents of the town in his target population. The sample must come from the directory and each person in the directory should have an equal chance of being selected. The incorrect options are too narrowly focused and are not representative of the town.

Example Question #1 : How To Define A Sample Set

Which of the following is a continuous variable?

i. The average weight of a newborn puppy

ii. The number of snow days during the last month

iii. The amount of time that it takes to read a book

 

Possible Answers:

i only

i and iii

None of the above

i and ii

ii and iii

Correct answer:

i and iii

Explanation:

A continuous variable can take on an infinite continuum of possible real number values. Weight and the amount of time to read a book are continuous because it is impossible to write down all the distinct potential values. 

Example Question #2 : How To Define A Sample Set

For which of these is a binomial probability model most reasonable?

Possible Answers:

The number of people surveyed until someone who has no pets is found. 

The number of times, out of  attempts, that a player can throw a basketball through the hoop from  feet away.

The colors of the gummy bears in a particular bag of gummy bears from a randomly selected store rack. 

The number of cards drawn from a deck until the two jokers are drawn. 

The number of times a randomly selected college student has gone to the beach in the last year. 

Correct answer:

The number of times, out of  attempts, that a player can throw a basketball through the hoop from  feet away.

Explanation:

A binomial model counts the number of successes out of a specific number of attempts at a task when each attempt has a constant probability of success. The correct choice is the one that specifies the number of attempts. 

Example Question #1 : How To Do A Random Selection For A Survey

Which of the following is the best way to ensure a sample is representative and unbiased?

Possible Answers:

Take a voluntary response sample

Take a random sample

Take a census

Take a convenience sample

None of the other answers

Correct answer:

Take a random sample

Explanation:

Taking a random sample is the only data-collecting method that ensures that every set of individuals has an equal chance of being selected for the sample and does not introduce any significant bias. Taking either a voluntary response sample or a convenience sample does not ensure these important aspects, as there is some unwanted selectivity involved in the data being collected. Taking a census is inferior to taking a sample of any sort, as it is both costly and time-consuming.

Example Question #2 : How To Do A Random Selection For A Survey

John would like to find out what percentage of residents in his neighborhood enjoy shopping. Which of the following is the best method to randomly select participants to take John's survey? 

Possible Answers:

John can go to his local mall and survey individuals at random to determine if they enjoy shopping

John can sit at the park in his neighborhood and survey every individual that passes by to determine if they enjoy shopping

John can number residents his neighborhood and randomly select residents to survey using a random number generator

There is no effective way to randomly select participants to be surveyed

John can go to his local grocery store and survey individuals at random to determine if they enjoy shopping

Correct answer:

John can number residents his neighborhood and randomly select residents to survey using a random number generator

Explanation:

The best answer is the choice that reduces the amount of bias in the selection of survey participants. Surveying local residents at a grocery store, neighborhood park, or shopping mall would introduce selection bias into the survey since every member of the target population does not have an equal chance of being selected. Using the random number generator, every single person in the neighborhood has an equal chance of being selected to take the survey.

Example Question #1 : How To Conduct A Sample Survey

To find the percentage of households in a town who own more than one motor vehicle, a survey will ask the next 100 drivers at a popular gas station if there is more than one motor vehicle in their household. Is this survey biased and if so, what is the main type of bias?

Possible Answers:

None of the other answers are correct

Yes, undercoverage bias

Yes, voluntary response bias

Yes, non-response bias

No, the survey is representative of the local population

Correct answer:

Yes, undercoverage bias

Explanation:

Because the survey is being conducted on drivers at a gas station, people/households who do not own a motor vehicle will not be included in the survey.

Example Question #1 : How To Identify Sources Of Bias In A Survey

Identify the type of bias:

A researcher wants to know what proportion of coffee drinkers would pay more than $5 for a coffee drink. The researcher asks the following question:

"Do you agree that $5 is way too much to pay for a simple coffee"

Possible Answers:

Voluntary response bias

Undercoverage

Leading question

Nonresponse bias

Social desirability

Correct answer:

Leading question

Explanation:

By using the words way too much and simple coffee, the researcher is introducing bias into their question by causing people to favor one response over another.

To avoid this sampling bias, the researcher should use more neutral wording, such as "Agree or diasgree- I would pay $5 or more for a coffee drink."

Example Question #111 : Data

Identify the type of bias:

A researcher wants to know whether students at a particular university have ever cheated on a test. The researcher walks up to 100 random students and asks them the following question:

"Have you ever cheated on a test or exam?"

Possible Answers:

Social desirability

Voluntary response bias

Nonresponse bias

Undercoverage

Leading questions

Correct answer:

Social desirability

Explanation:

Many people are reluctant to be honest about their bad behaviors, especially if they don't believe the survey is confidential. This will cause participants to be more likely to respond with whatever is more socially acceptable.

Example Question #31 : Data Collection

The best way to reduce variability in an unbiased sample is to __________.

Possible Answers:

take a bigger sample

take a random sample of any sort

There is no way to reduce variability in an unbiased sample

take a smaller sample

None of the other answers

Correct answer:

take a bigger sample

Explanation:

Using random sampling methods alone does not reduce variability in a sample; they only reduce bias. The best way to reduce variability in an unbiased sample is to take a bigger sample—the bigger the population of the sample, the less widespread the results will be. It is important to remember that if there is bias present in a sample, a large sample population size (n value) will not be enough to overcome the bias.

Example Question #1 : How To Identify Sources Of Bias In A Survey

Identify the type of bias:

A radio station polls listeners on a controversial issue by talking to people who call in to the station.

Possible Answers:

No bias

Voluntary response bias

Nonresponse bias

Leading questions

Undercoverage bias

Correct answer:

Voluntary response bias

Explanation:

Voluntary response bias usually results when those sampled are volunteers who select themselves.
Voluntary response bias can cause results to over represent those who have a strong opinion.

Learning Tools by Varsity Tutors