In this chapter
- The central limit theorem in depth
- Practical applications of the theorem, such as confidence intervals for means and proportions
- Estimating a population mean or proportion from a sample with a range of values using confidence intervals
- Handling smaller sample sizes using the t-distribution
In statistics, we rarely have access to a whole population, which is why we resort to sampling to estimate its characteristics. With a sample, we try to infer attributes of the larger population, assuming that the sample is representative. But a good statistician more often responds with uncertainty than with absolute certainty, embracing tools that allow for a range of values rather than a single one. Confidence intervals provide that range, giving us a way to express both our estimate and the uncertainty around it.
After studying the central limit theorem (CLT) in the last chapter, you might see where this is going. With a sample, we expect the mean to fall approximately within a normal distribution of sample means. Because it is part of a normal distribution, we can capture ranges using the bell curve.
