Part III Inferential Statistics
We are now ready to make (some) inferences about the real world based on data — this subject is called inferential statistics. We have seen how to display and interpret 1- and 2-variable data. We have seen how to design experiments, particularly experiments whose results might tell us something about cause and effect in the real world. We even have some principles to help us do such experimentation ethically, should our subjects be human beings. Our experimental design principles use randomness (to avoid bias), and we have even studied the basics of probability theory, which will allow us to draw the best possible conclusions in the presence of randomness.
What remains to do in this part is to start putting the pieces together. In particular, we shall be interested in drawing the best possible conclusions about some population parameter of interest, based on data from a sample. Since we know always to seek simple random samples (again, to avoid bias), our inferences will never be completely sure, instead they will be built on (a little bit of) probability theory.
The basic tools we describe for this inferential statistics are the confidence interval and the hypothesis test (also called test of significance). In the first chapter of this Part, we start with the easiest cases of these tools, when they are applied to inferences about the population mean of a quantitative RV. Before we do that, we have to discuss the Central Limit Theorem [CLT], which is both crucial to those tools and one of the most powerful and subtle theorems of statistics.
