The central idea of this chapter is that making the leap from sample to population carries a certain amount of uncertainty with it. In order to be good, honest analysts, we need to be able to express and quantify this uncertainty.
The example we chose to illustrate this principle was estimating population mean from a sample's mean. You learned that the uncertainty associated with inferring the population mean from sample means is modeled by the sampling distribution of the sample means. The central limit theorem tells us the parameters we can expect of this sampling distribution. You learned that we could use these parameters on their own, or in the construction of confidence intervals, to express our level of uncertainty about our estimate.
I want to congratulate you for getting this far. The topics introduced in this chapter are very often considered the most difficult to grasp in all of introductory data analysis.
Your tenacity will be greatly rewarded, though; we have laid enough...