AP Statistics : Data

Study concepts, example questions & explanations for AP Statistics

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Example Questions

Example Question #11 : How To Conduct A Sample 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:

Nonresponse bias

No bias

Voluntary response bias

Leading questions

Undercoverage

Correct answer:

Undercoverage

Explanation:

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 #4 : 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:

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

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

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

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

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

Correct answer:

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

Explanation:

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 in a random area of the cafeteria at the high school

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

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

Choosing  students at random from the high school 

Correct answer:

Choosing  students at random from the high school 

Explanation:

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 at random from a specific grade level 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 high school 

Correct answer:

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

Explanation:

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:

Systematic Sampling

Group Sampling

Simple Random Sampling

Convenience Sampling

Stratified Random Sampling

Correct answer:

Stratified Random Sampling

Explanation:

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 local elementary school and perform the experiment there.

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

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

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 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

Explanation:

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 #12 : How To Conduct A Sample Survey

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 different groups and select 25 houses at random from each group to survey 

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

Kevin could survey every third house 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 homogeneous groups and choose one group at random to survey houses within

Correct answer:

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

Explanation:

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. 

Example Question #1 : How To Find Descriptive Data From A Z Score

There are four suspects in a police line-up, and one of them committed a robbery. The suspect is described as "abnormally tall". In this case, "abnormally" refers to a height at least two standard deviations away from the average height. Their heights are converted into the following z-scores:

Suspect 1: 2.3

Suspect 2: 1.2

Suspect 3: 0.2

Suspect 4: -1.2. 

Which of the following suspects committed the crime? 

Possible Answers:

Suspect 4

Suspect 3

Suspect 2

Suspect 1

Correct answer:

Suspect 1

Explanation:

Z-scores describe how many standard deviations a given observation is from the mean observation. Suspect 1's z-score is greater than two, which means that his height is at least two standard deviations greater than the average height and thus, based on the description, Suspect 1 is the culprit. 

Example Question #1 : Basic Statistics

A value has a -score of .  The value is . . .

Possible Answers:

two standard deviations from the population mean

below the population mean

one standard deviation from the population mean

the same as the population mean

above the population mean

Correct answer:

below the population mean

Explanation:

The -score indicates how close a particular value is to the population mean and whether the value is above or below the mean.  A positive -score is always above the mean and a negative -score is always below it.  Here, we know the value is below the mean because we have a negative -score.

Example Question #2 : How To Find Descriptive Data From A Z Score

All of the students at a high school are given an entrance exam at the beginning of 9th grade. The scores on the exam have a mean of  and a standard deviation of . Sally's z-score is . What is her score on the test?

Possible Answers:

Correct answer:

Explanation:

The z-score equation is .

To solve for  we have .

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