AP Statistics : Data
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Example Questions
Example Question #1 : How To Identify The Placebo Effect In An Experiment
To test if vitamin C actually makes people feel better, a vitamin company decides to run a 5-day study where they give one group of 100 sick participants vitamin C pills and another group of 100 sick people placebo pills, and monitored another group of 100 sick people who took no pills.
At the end of the 5-day experiment, 90 participants in the vitamin C group reported feeling better. 30 participants in the no-pill group felt better after the 5-day period. Interestingly, 50 participants in the placebo group felt better after the 5-day period.
What could explain these numbers?
5 days is too long for the experiment.
The placebo effect: some participants in the placebo group began to feel better because they thought they were taking something that would help them.
Vitamin C actually makes people feel sicker.
5 days is too short for the experiment.
There is no logical explanation.
The placebo effect: some participants in the placebo group began to feel better because they thought they were taking something that would help them.
The placebo effect is when effects are seen in a group of people who did not actually receive a treatment.
In the vitamin C group, 90 participants felt better.
Naturally (no-pill), 30 participants felt better.
With the placebo, 50 participants felt better. Since more people felt better with the placebo than with no treatment at all, it appears that some percentage of people believed that they would feel better with a pill and actually began to feel better due to the placebo effect.
Example Question #11 : How To Conduct An Experiment
A study is attempting to test various brands of cola against each other. Which of these would not be a measure that could be used to help create a double blind test?
Serving the samples to the taster in their usual containers.
Randomizing the placement of the cola samples.
Making sure the test administrator also does not know the brand of each sample until after the test.
Removing or covering up the labels on the cans or bottles.
Filling the sample cups the same way.
Serving the samples to the taster in their usual containers.
Remember that a double blind experiment means that neither the subject nor the person conducting the experiment knows the identity of the various treatments until the test is over, so as to minimize bias.
Therefore of the options,
serving the samples to the taster in their usual containers, is the one which would not help create a double blind test.
Example Question #2 : How To Establish Blind Experiments
Which of the following is an example of a double blind experiment?
An experiment in which researchers know which therapy test subjects are receiving, but test subjects are unaware
An experiment in which both test subjects and researchers are aware of who is receiving the treatment and who is receiving the placebo
An experiment in which neither the test subjects nor the researchers know who is receiving the treatment and who is receiving the placebo
An experiment in which test subjects know which therapy they are receiving, but researchers are unaware
None of these are an example of a double blind experiment
An experiment in which neither the test subjects nor the researchers know who is receiving the treatment and who is receiving the placebo
A double blind experiment requires that both researchers and test subjects are unaware of who is receiving the treatment and who is receiving the placebo. If only one group is unaware, it is a single blind experiment. If both groups are aware, the experiment is not blinded.
Example Question #302 : Ap Statistics
Which of the following is an example of a single-blind experiment?
An experiment in which the researchers and test subjects are unaware of who is receiving a placebo and who is receiving a therapy.
An experiment in which the researchers and test subjects are aware of who is receiving a placebo and who is receiving a therapy.
An experiment in which the test subjects are aware of who is receiving a placebo and who is receiving a therapy, but the researchers are unaware.
Two of the answers are correct
An experiment in which the researchers are aware of who is receiving a placebo and who is receiving a therapy, but the test subjects are unaware.
Two of the answers are correct
In a single-blind experiment, one group (either the researchers or the test subjects) must be blinded while the other group is aware of who is receiving a placebo and who is receiving a therapy.
The following two examples are correct:
-An experiment in which the test subjects are aware of who is receiving a placebo and who is receiving a therapy, but the researchers are unaware.
-An experiment in which the researchers are aware of who is receiving a placebo and who is receiving a therapy, but the test subjects are unaware.
Example Question #1 : How To Establish Blind Experiments
Alpha Corporation developed a new pill to treat elevated glucose levels. They want to test the efficiency of the pill to lower glucose levels by gathering a sample of people with high glucose and giving them either:
1) A daily dose of their new pill ("Experimental Group")
2) A daily placebo pill that looks the same but does not do anything ("Placebo Group")
How can they make this a "Blind Study"?
Give all participants both pills.
Give the pill to people with high blood glucose and low blood glucose.
Randomly sort people into the Experimental or Placebo groups, without letting them know which pill they received.
Blindfold the participants while they take the pills.
Keep the participant identities hidden from the experimenters permanently.
Randomly sort people into the Experimental or Placebo groups, without letting them know which pill they received.
A blind experiment is one in which the participant does not know which experimental group they are in-- which is accomplished by not letting them know if they are in the Experimental or Placebo group.
Example Question #2 : How To Establish Blind Experiments
A drug company wants to test a new pill that should make people's nails grow twice as quickly as normal. How can they make the study a blind study?
Give half participants the placebo pill and tell them they had the actual pill, and give the rest the actual pill but tell them they have the placebo pill.
This test cannot be done as a blind study.
Give all participants the placebo pill and measure nail growth.
Give all participants the actual pill and measure nail growth.
Give one group of people the actual pill and one group a placebo, but don't tell the participants which pill they are receiving.
Give one group of people the actual pill and one group a placebo, but don't tell the participants which pill they are receiving.
In order for a study to be "blind," the participants can't know which group they are sorted into. For a study to be double-blind, which is even better, the researchers should also be blind to which group participants are in until the study is completed.
Example Question #1 : How To Conduct Matched Pairs Experiments
An company wants to test how much a fuel additive improves the fuel efficiency of cars and has 
Chi-square test of association
Matched pairs 
Two-sample 
One-sample proportion 
Two-sample 
Matched pairs
A matched pairs design t test is the best choice because it will compare the effectiveness of the fuel additive by looking at the means differences of two sample sets where the only variable that is changed from one test to the other test is the introduction of the fuel additive. It makes no sense to compare the performance of, for example, a Ford Mustang with the additive against a Toyota Prius hybrid without the additive. It becomes crucial to compare fuel efficiency with and without the fuel additive for each car.
Example Question #1 : How To Conduct Matched Pairs Experiments
For which of these experiments would a matched pairs design not be ideal?
Comparing effectiveness of two coaches and their methods.
Comparing strength of right arms against strength of left arms.
Evaluating effectiveness of a test preparation regimen.
Evaluating the effectiveness of a diet.
Evaluating effectiveness of a new type of oil filter in various cars.
Comparing effectiveness of two coaches and their methods.
Remember that a matched pairs design tends to involve "before and after" or "with and without" or "left and right" using the same experimental units.
Therefore comparing effectiveness of two coaches and their methods would not be an experiment for the matched pairs design.
Example Question #1 : How To Define A Survey Population
A company asks you to conduct a survey to discover what consumers generally want. What should the survey population be?
Past consumers
All of the company's customers
All possible consumers
Future consumers
All possible consumers
The company wants a survey on what consumers want. That means they are interested in all possible consumers. The other groups are too specific.
Example Question #1 : How To Conduct A Sample Survey
Your AP Statistics teacher asks you to conduct a survey to determine the most popular cereal brand at your high school. Which of the following should be the survey population in your study?
All students in your high school
All high school students in your city
Students in your AP Statistics Class
All high school students in the United States
Students in your grade level
All students in your high school
Since your teacher has asked that you determine the most popular cereal brand at your high school, the survey population should be limited to only your high school. Other students' preferences of cereal brands around the nation will have no impact on the survey results.
Additionally, surveying only students in your AP Statistics class or only students in a particular grade level would not be representative of all students in your high school. Therefore, the correct survey population is all students in your high school.
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