AP Statistics : How to conduct matched pairs experiments
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Example Question #311 : Ap Statistics
An company wants to test how much a fuel additive improves the fuel efficiency of cars and has 
One-sample proportion 
Two-sample 
Two-sample 
Chi-square test of association
Matched pairs 
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 strength of right arms against strength of left arms.
Evaluating the effectiveness of a diet.
Comparing effectiveness of two coaches and their methods.
Evaluating effectiveness of a new type of oil filter in various cars.
Evaluating effectiveness of a test preparation regimen.
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.
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