AP Statistics : AP Statistics

Study concepts, example questions & explanations for AP Statistics

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Example Questions

Example Question #2 : How To Conduct 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?

Possible Answers:

Experimental group

Placebo group

Neither

Control group

Correct answer:

Control group

Explanation:

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 : How To Define Experimental Units

Of the following examples, which best describes quantitative data?

Possible Answers:

A child's gender.

College grade level-freshman, sophomore, junior, or senior.

Temperature measurements of water in degrees Fahrenheit.

The softness of a chair.

A student's least favorite sport.

Correct answer:

Temperature measurements of water in degrees Fahrenheit.

Explanation:

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?

Possible 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 use chance to randomly assign experimental units to treatment groups (or vice versa)

To increase the number of experimental units

None of the other answers

To hold an extraneous variable constant

Correct answer:

To separate a particular sample into groups previously known to be similar in some way that are expected to affect response to treatments

Explanation:

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? 

Possible Answers:

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

Correct answer:

The gender of a high school student

Explanation:

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 #91 : Data

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?

Possible Answers:

Flipping a coin

Assigning the treatment based on who needs it the most 

Assigning the treatment by gender

Obtaining nationally representative samples for both

Correct answer:

Flipping a coin

Explanation:

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. 

Possible Answers:

Convenience Sampe

Stratified random sample

Cluster sample

Multistage sample

Simple random sample

Correct answer:

Convenience Sampe

Explanation:

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 : Data Collection

Which of the following experiments has the least amount of bias? 

Possible Answers:

A survey of how many people enjoy shopping conducted at a shopping mall. 

A survey of the number of people that watch online TV conducted using email. 

None of these examples contain any potential bias. 

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 randomized double-blind experiment in which test subjects are assigned to either a placebo or a therapeutic agent that is used to improve metabolism. 

Correct answer:

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. 

Explanation:

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?

Possible Answers:

The original recipe has the company's name on it, but the new sample does not.

There are not many taste-testers who are qualified to evalutate food.

Some people may wish they were eating a different dessert.

There is no bias.

People may not all like chocolate to the same degree.

Correct answer:

The original recipe has the company's name on it, but the new sample does not.

Explanation:

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 #92 : Data

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?

Possible Answers:

The group receiving the new device should simply receive the device without being asked to stay hydrated.

Participants should be able to choose which device is right for them.

The group receiving the old device should also be required to stay hydrated.

Correct answer:

The group receiving the old device should also be required to stay hydrated.

Explanation:

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? 

Possible Answers:

Lung Cancer

None of these are potential confounding variables

Caffeine Consumption

Medical Researchers

Smoking

Correct answer:

Smoking

Explanation:

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. 

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