AP Statistics : Data Collection

Study concepts, example questions & explanations for AP Statistics

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Example Questions

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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 a high school 

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

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 

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:

Simple Random Sampling

Convenience Sampling

Group Sampling

Stratified Random Sampling

Systematic 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 #123 : Data

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.

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

Find a local elementary school and perform the experiment there.

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

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

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 #124 : Data

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

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

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

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 Conduct An Observational Study

You are conducting the following series of observational studies to determine if generally understood parameters about a local population are accurate:

A. You stand on the sidewalk next to a stop sign to observe and record the number of cyclists and drivers who stop or don't stop.

B. You inform customers at a local fast food restaurant of your study to determine the proportion of healthy food choices from the menu and then observe their choices.

C. From your car in the mall parking lot, you observe the proportion of shoppers who hold the door open for the next person who enters or exits the mall.

D. To estimate the proportion of males and females in the local community, you observe spectators at a hockey match and count and record the gender in a randomly selected area of the crowd.

E. You review the daily sign-in sheets at a local fitness center to estimate the average number of workouts per week for residents of the local community.

Which observational study should yield the most accurate results?

 

Possible Answers:

Study D

 

Study C

Study A

Study E

Study B

Correct answer:

Study C

Explanation:

Study C takes a representative sample of local residents, and it does so without affecting the outcomes.

Studies A and B are influenced by the person conducting the survey. Studies D and E are biased samples of the population.

Therefore, C should yield the most accurate results.

Example Question #1 : How To Conduct An Observational Study

What situation would most warrant the method of observational study to produce accurate results?

Possible Answers:

Testing the effectiveness of a new drug.

Observing how chocolate consumption affects mood.

None of the above.

Studying the relationship between sleep deprivation and cold susceptibility.

Studying the social interactions between groups of baboons.

Correct answer:

Studying the social interactions between groups of baboons.

Explanation:

Obseverational study does not involve any interference with the group being studied, so watching baboons in their natural habit would be best suited for this method.

Example Question #1 : How To Conduct A Census

Kate would like to determine what flavors of ice cream are most popular among students in her AP Statistics class. In total, there are 100 students in the class. Which of the following would be an appropriate sampling methodology? 

Possible Answers:

There is no effective way to obtain a representative sample from the target population 

Group students into several homogeneous groups and choose one group to survey in order to determine the class's favorite ice cream flavor

Ask every fifth person that walks through the door what their favorite flavor of ice cream is before class starts

Randomly select several of the most popular students in the class to answer questions about their favorite ice cream flavor

Obtain a census of the class and survey each person in the class to determine their favorite flavor of ice cream

Correct answer:

Obtain a census of the class and survey each person in the class to determine their favorite flavor of ice cream

Explanation:

In this situation, it is best to conduct a census in order to determine what the class's favorite flavor of ice cream is. Since there are only 100 students in the class, a sample of the class would be very small and may not be representative of the class as a whole. 

Example Question #1 : Census And Studies

Census is to __________ as survey is to __________.

Possible Answers:

cluster; stratum

There are no similarities between these two.

population; sample

population; group

sample; population

Correct answer:

population; sample

Explanation:

A census gathers data from an entire population of people. A survey targets a representative sample of a population.

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