Statistical Inference: A Short Course

9.4 A Sample Size Requirements Formula

Given Equation (9.16), let us solve for n or

(9.17)

Let us refer to this expression as the sample size requirements formula. What are the requirements? As noted above when employing Equation (8.9), they are “precision” and “reliability.” Hence Equation (9.17) provides us with the sample size required for a degree of precision of ±w/2 with 100(1 − α)% reliability. (Note that w/2 should always be expressed as a decimal.)

Example 9.4

Suppose we would like to estimate the proportion of individuals with a particular characteristic to within ±3% of p (the population proportion of individuals displaying this characteristic) with 95% reliability. How large of a sample should be taken? Here = = 1.96 and ±w/2 = ±0.03. Then from Equation (9.17),

Since we do not as yet have our sample, we cannot determine . (It seems we have found ourselves “up a tree without a creek.”) There are three possible ways to resolve this difficulty:

1. Use a prior estimate of