# AP Statistics : How to conduct matched pairs experiments

## Example Questions

### 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  cars of various makes and models available to test. Which experimental design would be most appropriate?

Two-sample -test

Matched pairs -test

One-sample proportion -test

Chi-square test of association

Two-sample -test

Matched pairs -test

Explanation:

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 #2 : How To Conduct Matched Pairs Experiments

For which of these experiments would a matched pairs design not be ideal?

Evaluating effectiveness of a test preparation regimen.

Comparing strength of right arms against strength of left arms.

Evaluating effectiveness of a new type of oil filter in various cars.

Evaluating the effectiveness of a diet.

Comparing effectiveness of two coaches and their methods.

Comparing effectiveness of two coaches and their methods.

Explanation:

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.