Lesson 34: Sample Size

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question markIntroduction

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 μ, a proportion p, and a standard deviation σ. 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! Specifically, we'll:

  • derive a formula for the sample size, n, necessary for estimating the population mean μ
  • 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.