# The t-test for the equality of two means

• George Argyrous
Chapter

## Abstract

All the tests covered thus far have been dealing with the one-sample case. That is, they all involve making an inference about one population only: we don’t have information about the population, so we infer it from the sample result. We make this inference so that we can compare the result with another population for which we do have information. But what if we don’t have information about this other population either? In this situation we have to make an inference about this second population as well. For example, in Chapter 10 we worked through an example where we were interested in the average amount of television watched by Australian and British children between the ages of 5 and 12 years. We would have liked to compare the population parameters, but unfortunately we only had population values for British children. For Australian children we took a sample of 20 and made an inference based on this sample result. However, what if we did not have information on the population of British kids either? The best we could do would be to take a random sample of British children as well, and make another inference from this second sample. In such a situation we would have to conduct a two-sample test of significance (Figure 13.1).

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