Our final example of inductive logic denies that we make inferences at all. Instead, we behave inductively, in such a way that our system for making decisions has good overall consequences for us. This is the theory of confidence intervals.
SAMPLES AND POPULATIONS
In Chapter 2 there was a box of 60 oranges–a population of oranges. We drew 4 oranges at random–a sample. In Chapter 2 we distinguished two forms of argument:
Statement about a population.
So,
Statement about a sample.
Statement about a sample.
So,
Statement about a population.
Bernoulli's Theorem, applied to sampling with replacement from an urn, makes a statement about a sample on the basis of knowledge about the population of the urn and the sampling method. It is an example of the first type of argument.
Now we want to go in the other direction. We take a sample. We want to draw a conclusion about a population. A significance test involves one type of reasoning but does not go very far. We often want to use a sample to estimate something about a population. The most familiar type of estimate based on a sample is the opinion poll.
OPINION POLLS
Before we do some inductive logic, we should pause to think realistically about survey sampling. Consider a controversial survey topic.
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