STATISTICAL APPLICATIONS

In a statistical generalization, we draw inferences concerning a population from information concerning a sample of that population. If 60 percent of the population sampled said that they would vote for candidate X, we might draw the conclusion that roughly 60 percent of the population will vote for candidate X. With a statistical application (sometimes called a statisti- cal syllogism), we reason in the reverse direction: From information concern- ing a population, we draw a conclusion concerning a member or subset of that population. Here is an example:

Ninety-seven percent of the Republicans in California voted for McCain. Marvin is a Republican from California.

Marvin voted for McCain.

Such arguments have the following general form:

X percent of Fs have the feature G. a is an F. a has the feature G.4

5. I’ve never tried it before, but I just put a kiwi fruit in a tub of water. It floated. So most kiwi fruits float in water.

6. I have lots of friends. Most of them think that I would make a great president. So most Americans would probably agree.

7. In exit polls after people had just voted, most people told our candidate that they voted for her, so probably most people did vote for her.

8. Mary told me that all of her older children are geniuses, so her baby will probably be a genius, too.

9. When asked whether they would prefer a tax break or a bloated budget, almost everyone said that they wanted a tax break. So a tax break is over- whelmingly popular with the people.

10. When hundreds of convicted murderers in states without the death penalty were asked whether they would have committed the murder if the state had a death penalty, most of them said that they would not have done it. So most murders can be deterred by the death penalty.

It is often easy to see that a sample is biased, but how can you tell that a sam- ple is not biased? How can you determine whether a sample is big enough?