The other type of inference is hypothesis testing. Though hypothesis testing and interval estimation use similar mathematics, they make quite different inferences about the population. Estimation makes no prior statement about the population; it is designed to make an educated guess about a population that you know nothing about. Hypothesis testing tests to see if the population has a certain characteristic—say a certain mean. This works by using statisticians' knowledge of how samples taken from populations with certain characteristics are likely to look to see if the sample you have is likely to have come from such a population.
A simple example is probably the best way to get to this. Statisticians know that if the means of a large number of samples of the same size taken from the same population are averaged together, the mean of those sample means equals the mean of the original population, and that most of those sample means will be fairly close to the population mean. If you have a sample that you suspect comes from a certain population, you can test the hypothesis that the population mean equals some number, m, by seeing if your sample has a mean close to m or not. If your sample has a mean close to m, you can comfortably say that your sample is likely to be one of the samples from a population with a mean of m.
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