AP Statistics : Data
Study concepts, example questions & explanations for AP Statistics
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Example Questions
Example Question #1 : How To Conduct 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.
Example Question #1 : How To Identify Sources Of Bias In An Experiment
A major chocolate company wants to test the effects of adding more sugar to their standard chocolate bar to see if customers enjoy it more.
They select 10 subjects to randomly participate in a taste test. They bring in samples of their original product, which is sold in tiny squares that says the company's name on them, and samples of the increased-sugar versions, which are plain chocolate squares of the same size. The company asked participants to taste both chocolates and rank how much they like them on a scale of 1 to 10.
Which of the following represents a possible source of bias in the study?
There is no bias.
Some people may wish they were eating a different dessert.
People may not all like chocolate to the same degree.
There are not many taste-testers who are qualified to evalutate food.
The original recipe has the company's name on it, but the new sample does not.
The original recipe has the company's name on it, but the new sample does not.
The presence of the company's name on the original sample may be a soure of bias. If people already have a preexisting opinion about the brand, they may rate that chocolate as better or worse based on those opinions rather than flavors.
Example Question #11 : Data Collection
Let us suppose a company wants to evaluate whether a new medical device works better than current devices. It conducts a small experiment to assess the effectiveness of the new device. To conduct the experiment, the company randomly assigns one group to the new medical device, which requires users to stay well hydrated, and the other group to the old device.
How should we control for confounding variables?
Participants should be able to choose which device is right for them.
The group receiving the new device should simply receive the device without being asked to stay hydrated.
The group receiving the old device should also be required to stay hydrated.
The group receiving the old device should also be required to stay hydrated.
When comparing the effectiveness of a treatment, one should try to ensure that only the treatment varies across groups. In this case, the new device is compared to an old device. However, the new device also requires that users stay well hydrated. If we observe any positive effects from the new device, we won't know whether the new device is effective, or if merely staying well hydrated is actually what is effective. To rule out this confounding variable, we should also ask the group using the old machine condition to stay hydrated as well.
Example Question #1 : How To Identify Confounding Factors In An Experiment
An experiment was done by medical researchers to determine the association between drinking caffeine and severity of lung cancer. Results showed that there was a high association between the two variables. Which of the following could be a potential confounding variable in the experiment?
Medical Researchers
Caffeine Consumption
Smoking
None of these are potential confounding variables
Lung Cancer
Smoking
A confounding variable is one that could potentially have an effect on both the independent and dependent variables in a study. In this case, it is possible that there is an association between smoking and caffeine as well as smoking and lung cancer.
Example Question #1 : How To Identify Confounding Factors In An Experiment
A study finds that caffeine intake has a strong positive correlation with grades for college students. In other words, on average, the more caffeine intake a student has, the higher a grade the student gets.
Which of the following could potentially be a confounding variable in this experiment?
The amount of soda that each student consumes
Amount of sleep a student gets each night
The caffeine intake of students
The grade a student receives
The amount of coffee that each student drinks
Amount of sleep a student gets each night
The only confounding variable in this experiment is the amount of sleep that each student gets. A confounding variable is one that has an impact on both the dependent and independent variable. It is possible that the amount of sleep a student gets is related to caffeine intake, which in turn affects the grade a student receives on a test or assignment.
Example Question #12 : How To Conduct An Experiment
An experiment testing the effects of caffeine on endurance performance in athletes assigns caffeine to a randomly selected group of athletes and has them exercise. Another trial was conducted in which the same group exercised without anything given to them to take. The results did not match the expected results. What should be done to improve this experiment?
Nothing, the experiment is sound
Caffeine may affect different people in different ways, so varying amounts of caffeine should be administered.
The group should be randomly selected from a population of athletes and non-athletes, not just athletes.
A different group should be used for each trial because the athletes' first trial may have influenced their second trial.
There may a placebo effect with the caffeine, so an identical application without caffeine should be given to the control group.
There may a placebo effect with the caffeine, so an identical application without caffeine should be given to the control group.
The placebo effect can potentially be a confounding variable. By knowingly taking a substance, participants may feel more energenized. By administering the same substance both trials, with the only thing changed being caffeine content, this corrects for this possible confounding variable.
Example Question #1 : How To Identify Confounding Factors In An Experiment
A small local umbrella company is trying to test the effectiveness of their umbrellas by looking at how many umbrellas they sell each year.
In 2014, the company sold 2,000 umbrellas.
In 2015, they sold 1,500 umbrellas.
They assume that their umbrellas are less effective which is why sales decreased.
However, there could be many confounding factors. Which of the following is NOT a possible confounding factor?
There may have been less rain in 2015 than in 2014, therefore decreasing the need for umbrellas.
An increase in prices may have led to decreased sales.
There are no confounding factors.
If the same people live in the city during 2014 and 2015, people may already have umbrellas in 2015 and might not need to buy them.
Three of these could be confounding factors.
Three of these could be confounding factors.
Any of these answers could explain why umbrella sales dropped. You cannot assume any specific cause explains a change in data like this-- further experimentation should be done rather than assuming cause and effect.
Example Question #11 : Data Collection
A study is trying to determine if a particular medication (Y) is effective in weight loss. Patients participating in the study were randomly assigned to groups A, B, C, D, or E. Group A will receive one dose of Y, Group B will receive two doses of Y, Group C will receive three doses of Y, Group D will receive four doses of Y, and Group E will serve as the control group.
Which group will be receiving the placebo (a sugar pill)?
Group E
Group D
Group B
Group C
Group A
Group E
The control group in an experiment typically receives placebo treatments (in this case - Group E). Since all of the other groups are receiving at least one dose of the medication, they are considered to be experimental groups.
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