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A lot of material has been covered in this chapter, and not much of it has been easy. We are getting into real statistics now, and it will require care on your part if you are going to keep making sense of statistics.
The chapter outline is simple:
- Many things are distributed the same way, at least once we've standardized the members' values into z-scores.
- The central limit theorem gives users of statistics a lot of useful information about how the sampling distribution of is related to the original population of x's.
- The t-distribution lets us do many of the things the central limit theorem permits, even when the variance of the population, sx, is not known.
We will soon see that statisticians have learned about other sampling distributions and how they can be used to make inferences about populations from samples. It is through these known sampling distributions that most statistics is done. It is these known sampling distributions that give us the link between the sample we have and the population that we want to make an inference about.
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