AP Statistics : Data Collection
Study concepts, example questions & explanations for AP Statistics
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Example Questions
Example Question #1 : Data Collection
A drug company wants to test whether its medication reduces cancer risk. Assuming the company conducts an experiment in which participants are randomly assigned to treatment and control groups, what would the appropriate control group look like?
Those assigned to the control take the medication and then suddenly discontinue taking it.
Those assigned to the control take a sugar pill.
Those assigned to the control take the medication throughout the study period.
Those assigned to the control take a sugar pill.
The only thing you want to vary across groups when you're conducting an experiment is the treatment. Since taking pills is a part of taking medication (the treatment), medical experiments often employ something called a placebo-controlled study where outcomes for those who are randomly assigned to take the medication are compared to outcomes for those who are randomly assigned to take a sugar pill. The sugar pill is expected to have no effect, so it serves as a useful baseline to compare the treatment to.
Example Question #1 : How To Define Control Groups In An Experiment
In a public health study, researchers want to see how the addition of fresh produce stands in inner cities can affect the body weights of people who live within 1 mile of the stands.
The research group gathers data from several groups. Please identify which is the Control group.
Area A received a brand new fresh fruit and vegetable stand.
The researchers gathered information on body weight of people living within 1 mile of this area's central location, both at the starting date and ending date of the study (1 year later).
Area B received a new fresh fruit and vegetable stand.
The researchers gathered information on body weight of people living within 1 mile of this area's central location, both at the starting date and ending date of the study (1 year later).
There is a small town nearby which has several produce stands but also received another new fruit and vegetable stand.
The researchers gathered information on body weight of people living within 1 mile of this area's central location, both at the starting date and ending date of the study (1 year later).
One area of the city received no fresh fruit and vegetable stand.
The researchers gathered information on body weight of people living within 1 mile of this area's central location, both at the starting date and ending date of the study (1 year later).
There is no control group in this study.
One area of the city received no fresh fruit and vegetable stand.
The researchers gathered information on body weight of people living within 1 mile of this area's central location, both at the starting date and ending date of the study (1 year later).
Areas A and B are both experimental areas, where they received the treatment (the new produce stand), so comparing body weights before and after the treatment will provide valuable data.
The area of the city which did not receive the treatment (a produce stand) will provide data of how body weight may change over time naturally, without the stand, in order to compare the effects of the stands elsewhere.
The nearby town already has produce stands and provides residents with a different food environment, so it cannot act as the control group. It has different conditions than the experimental areas A and B, so comparing it to these areas will not provide helpful data in terms of the treatment's effects.
Example Question #1 : How To Define Control Groups In An Experiment
You and your classmate want to test the effect of food coloring on plant color. One of the groups in the experiment receives dye-free water. Which group is this?
Control group
Placebo group
Experimental group
Neither
Control group
The control group receives no treatment.
The experimental group receives the treatment of the independent variable.
Because the flowers getting no dye do not receive the treatment, it is the control group.
Example Question #1 : How To Define Control Groups In An Experiment
You and your friend want to test the effect of different brands of fertilizer on sunflower height.
One group receives no fertilizer during the course of the experiment.
Which group is this?
Experimental group
Control group
Placebo group
Neither
Control group
The control group receives no treatment.
The experimental group receives the treatment of the independent variable.
Because the sunflowers getting no fertilizer do not receive the treatment, it is the control group.
Example Question #1 : Data Collection
Of the following examples, which best describes quantitative data?
College grade level-freshman, sophomore, junior, or senior.
A child's gender.
A student's least favorite sport.
The softness of a chair.
Temperature measurements of water in degrees Fahrenheit.
Temperature measurements of water in degrees Fahrenheit.
Quantitative data describes a certain type of information that can be counted or expressed numerically and can be used in meaningful computations. Quantitative data is different from qualitative data, which is primarily involved in describing things in terms of categorizations or specific qualities. Looking at the answer choices, it is clear that measuring the temperature of water in degrees Fahrenheit is a numerical piece of information, and is thus quantitative.
Example Question #2 : Data Collection
When designing an experiment, what is the purpose of blocking?
None of the other answers
To separate a particular sample into groups previously known to be similar in some way that are expected to affect response to treatments
To increase the number of experimental units
To hold an extraneous variable constant
To use chance to randomly assign experimental units to treatment groups (or vice versa)
To separate a particular sample into groups previously known to be similar in some way that are expected to affect response to treatments
The purpose of blocking, by definition, is to separate a particular sample into groups previously known to be similar in some way that are expected to affect response to treatments. The other choices pertain to control (keeping an extraneous variable constant), randomization (using random chance to assign experimental units to treatments), and replication (increasing the number of experimental units to reduce chance variation) in an experiment.
Example Question #1 : How To Define Experimental Units
Which of the following is an example of qualitative data?
The amount of carbon monoxide emissions in the air
The average SAT score of students at a particular high school
The temperature of a glass of water
The gender of a high school student
The speed at which a car is traveling
The gender of a high school student
The only example of qualitative data here is the gender of a high school student (i.e. male or female). This cannot be quantified, unlike the other answer choices which all have numbers, quantities, and amounts associated with them.
Example Question #1 : How To Do Random Assignments In An Experiment
A researcher wants to randomly assign participants to a treatment and control group. Which of the following approaches ensures that the treatment assignment is random?
Assigning the treatment based on who needs it the most
Obtaining nationally representative samples for both
Flipping a coin
Assigning the treatment by gender
Flipping a coin
The only random procedure here is the coin flip. In expectation, the coin flip ensures that no background variables influence treatment assignment whereas the other examples either have nothing to do with random assignment (e.g. nationally representative sample) or completely contradict the purpose of random assignment (e.g. assigning the treatment based on who needs it the most).
Example Question #1 : How To Identify Sources Of Bias In An Experiment
What type of sample was used in the following scenario:
Brad wants to know about the shopping habits of teenagers. He goes to the local mall and everytime he sees a teenager he asks them to fill out his survey. He spends one hour collecting responses on the top floor of the mall and one hour collecting responese on the bottom floor of the mall.
Multistage sample
Stratified random sample
Simple random sample
Cluster sample
Convenience Sampe
Convenience Sampe
The correct anwer is a convenience sample because the sample is drawn from a population that is close, readily available, and convenient. The sample does not represent the shopping behaviors of all teenagers.
Example Question #1 : How To Conduct An Experiment
Which of the following experiments has the least amount of bias?
A randomized double-blind experiment in which test subjects are assigned to either a placebo or a therapeutic agent that is used to improve metabolism.
A randomized double-blind experiment in which there are two experimental groups: Group A receiving a small dose of a particular drug and Group B receiving a large dose of a particular drug.
A survey of the number of people that watch online TV conducted using email.
A survey of how many people enjoy shopping conducted at a shopping mall.
None of these examples contain any potential bias.
A randomized double-blind experiment in which test subjects are assigned to either a placebo or a therapeutic agent that is used to improve metabolism.
The correct answer contains a control group and experimental group (placebo vs. therapeutic agent). Furthermore, it is randomized and double-blind.
The other incorrect choices introduce some form of bias - primarily selection bias in the two examples of surveys. The last example (the experiment with two experimental groups) does not have a control variable or placebo.
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