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So far we have tested sample means to ascertain how well they agree
with m of the underlying population. However,
we often want to compare the mean of different populations, e.g. compare
products of two different companies, or one medical therapy vs another,
etc. In effect, we use the same procedures as when inferring from a population.
Modifications have to be made to accommodate the fact that we are comparing
two estimated values and not an estimated with a true value.