Overview Section
So far, in this section, we have focused on using a random sample of size \(n\) to find an interval estimate for a variety of population parameters, including a mean \(\mu\), a proportion \(p\), and a standard deviation \(\sigma\). In none of our discussions did we talk about how large a sample should be in order to ensure that the interval estimate we obtain is narrow enough to be worthwhile. That's what we'll do in this lesson!
Objectives
Upon completion of this lesson, you should be able to:
- derive a formula for the sample size, \(n\), necessary for estimating the population mean \(\mu\)
- derive a formula for the sample size, \(n\), necessary for estimating a proportion \(p\) for a large population
- derive a formula for the sample size, \(n\), necessary for estimating a proportion \(p\) for a small, finite population
The methods that we use here in deriving the formulas could be easily applied to the estimation of other population parameters as well.