### All AP Statistics Resources

## Example Questions

### 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 census

None of the other answers

Take a convenience sample

Take a random sample

**Correct answer:**

Take a random sample

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 go to his local grocery store 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

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

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

**Correct answer:**

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

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 Identify Sources Of Bias In A 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:**

No, the survey is representative of the local population

Yes, non-response bias

None of the other answers are correct

Yes, voluntary response bias

Yes, undercoverage bias

**Correct answer:**

Yes, undercoverage bias

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 #2 : 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:**

Social desirability

Leading question

Undercoverage

Nonresponse bias

Voluntary response bias

**Correct answer:**

Leading question

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 #3 : How To Identify Sources Of Bias In A Survey

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:**

Undercoverage

Voluntary response bias

Leading questions

Social desirability

Nonresponse bias

**Correct answer:**

Social desirability

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 #4 : How To Identify Sources Of Bias In A Survey

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

**Possible Answers:**

take a smaller sample

take a random sample of any sort

There is no way to reduce variability in an unbiased sample

take a bigger sample

None of the other answers

**Correct answer:**

take a bigger sample

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 #5 : 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:**

Undercoverage bias

Voluntary response bias

No bias

Nonresponse bias

Leading questions

**Correct answer:**

Voluntary response bias

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.

### Example Question #6 : How To Identify Sources Of Bias In A Survey

Identify the type of bias:

A researcher wants to know what proportion of people in the United States favor student debt reform. The researcher goes to five universities and at each asks people whether they favor student debt reform.

**Possible Answers:**

Leading questions

Undercoverage

Nonresponse bias

No bias

Voluntary response bias

**Correct answer:**

Undercoverage

This is an example of undercoverage because the researcher did not speak to people who were not affiliated with a university. Therefore the researcher did not adequately sample all members of the overall population (people in the United States).

### Example Question #7 : How To Identify Sources Of Bias In A Survey

You are trying to conduct a survey of students within a college community to see if you should cut funding to the athletics department to save money. Which of the following manners of conducting this survey would lead to the least bias possible?

**Possible Answers:**

Go to the athletics department and survey 50 student athletes on the issue.

Randomly select a 300 student sample from all of the student body of the school and proctor the survey with those students.

Conduct a survey by having an open hotline where students may call in and give their opinion on the matter.

Pull 10 students aside as they walk across campus and ask them to take the survey.

Send out a questionnaire to randomly selected students and look at the ones that are sent back.

**Correct answer:**

Randomly select a 300 student sample from all of the student body of the school and proctor the survey with those students.

The correct answer (random sample of 300 students) includes a random sample which will reduce in bias and also is given to be done in person which reduces completion bias. It is also taken from the whole population of students and is a large sample which makes it a good representation of the population. Sending out a questionnaire has completion bias because the only people that will send it back will have strong and possibly biased beliefs already. The hot line has the same effect as those that have strong and biased opinions will be the ones to do it. Pulling students aside as they walk by is not a truly randomly constructed sample and using only 10 students is not a good representation of a whole college. Selecting a sample of just athletes is very biased as they will not want their programs cut.

### Example Question #1 : How To Do Simple Random Sampling

Which of the following is an example of simple random sampling at a high school?

**Possible Answers:**

Choosing students at random from a specific grade level of the high school

Choosing students at random from the high school

Choosing students at random from each of four different grade levels at the high school

Choosing students in a random area of the cafeteria at the high school

Choosing students at random from an AP Statistics class at the high school

**Correct answer:**

Choosing students at random from the high school

A simple random sample is obtained by randomly selecting individuals from a target population. Each individual in the target population (i.e. all students at the high school) should have an equal chance of being selected. Only one answer choice gives each high school student an equal chance of being selected: choosing students at random from the high school.