5 Sample size superpowers
This chapter covers
- The central limit theorem in depth, and how it connects to practical applications like confidence intervals for means and proportions
- How to estimate a population mean or proportion from a sample with a range of values using confidence intervals
- How to handle 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 characteristics of the population. With a sample, we try to infer attributes about the larger population, assuming that the sample is representative. However, a good statistician reacts more often with uncertainty than with absolute certainty, embracing tools that entertain a range of values rather than a single value. This is what confidence intervals accomplish.
After studying the central limit theorem in the last chapter, you might see where this is going. With a sample, we suspect the mean will fall approximately in a normal distribution of sample means. Because it is part of a normal distribution, we have the benefit of capturing ranges using the bell curve.