### All AP Statistics Resources

## Example Questions

### 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:**

Leading questions

No bias

Undercoverage bias

Nonresponse bias

Voluntary response bias

**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

No bias

Voluntary response bias

Undercoverage

Nonresponse 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:**

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.

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

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

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 the high school

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

Choosing students at random from a specific grade level of 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

**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.

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

Which of the following is an example of stratified random sampling when obtaining a sample of high school students?

**Possible Answers:**

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

Choosing students sitting in one random section of the cafeteria at a high school

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

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

Choosing students at random from a high school

**Correct answer:**

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

In order for there to be a stratified random sample, the target population must be split into different groups (i.e. grade levels). The sample population must be selected at random from each of these groups (i.e. choosing students from each of four different grade levels or groups). The other examples, although random, are not specifically stratified in their sampling methodology.

### Example Question #2 : How To Do Stratified Random Sampling

A study testing the effect of caffeine on mental performance invited participants for an experiment. The participants were selected randomly. people were selected from men who did not drink coffee. were selected from women who did not drink cofee. were selected from men who regularly drank coffee, and from women who regularly drank coffee. What type of sampling method is this?

**Possible Answers:**

Group Sampling

Systematic Sampling

Convenience Sampling

Stratified Random Sampling

Simple Random Sampling

**Correct answer:**

Stratified Random Sampling

Stratified Sampling is the method of randomly selecting subjects from various stratum, or subsets of the population. In this case, there were 4 stratum from which participants were randomly selected.

### Example Question #1 : How To Do Cluster Sampling

A researcherer wants to study the effectiveness of a certain curriculum program on kids' math scores, so she wants to implement the curriculum with kids in grades 2 to 4 to see if their scores significantly improve. To do so, she wants to try Random Cluster Sampling. How can she do this?

**Possible Answers:**

Find a list of all elementary schools in the state and then only look at schools with weak math programs before selecting which schools to run the experiment in.

Randomly select an elementary school from the entire list of elementary schools in the country

Find a local elementary school and perform the experiment there.

Select a "cluster" of schools in a local area.

Randomly select an elementary school in the country and ask the principal to recommend other schools that would be interested in participating.

**Correct answer:**

Randomly select an elementary school from the entire list of elementary schools in the country

Random sampling is a method in which every individual has an equal opportunity of being randomly chosen to participate in a study.

Cluster random sampling entails choosing from pre-formed "clusters"-- such as schools or hospitals-- and randomly selecting one of the clusters.

### Example Question #2 : How To Do Cluster Sampling

Kevin would like to find out what type of car is the most popular among residents in his neighborhood. There are 25 streets in his neighborhood and each street has approximately 12 houses on it. He would like to survey at least 120 houses before making a conclusion.

Which of the following is an example of random cluster sampling in Kevin's neighborhood?

**Possible Answers:**

Kevin could divide his neighborhood into five homogeneous groups and choose one group at random to survey houses within

Kevin could survey five houses at random on every single street in his neighborhood

Kevin could number each house from 1 to 300 and then randomly select 120 houses to survey using a random number generator

Kevin could divide his neighborhood into five different groups and select 25 houses at random from each group to survey

Kevin could survey every third house in his neighborhood

**Correct answer:**

Kevin could divide his neighborhood into five homogeneous groups and choose one group at random to survey houses within

In order for cluster sampling to be present, the entire population must be divided into homogeneous groups (known as clusters). For sampling purposes in this problem, clusters must be chosen as a simple random sample. There is only one answer choice that fits this pattern.

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