Let us arrange Equation (8.8) so as to obtain
What is the significance of this expression? Since our goal is to estimate the population mean μ, we should not simply start the estimation process by collecting some arbitrary number of observations on X and then determine either a point or interval estimate of μ. Sampling is not costless—there may be a sizable expenditure, stated in terms of dollars or effort or time, involved in collecting data. In this regard, even before any data collection is undertaken, we should have in mind certain target levels of precision and reliability that we would like to attain. This is where Equation (8.9) comes into play. It is called a sample size requirements formula because of the a priori requirements of precision and reliability imposed on the sampling process. Hence Equation (8.9) gives us the sample size required for a degree of precision of ±w/2 with reliability.
Let . How large of a sample should be taken so that the 95% confidence interval for μ will not be greater than 6 units in width or ? Here , and thus . Then and . From Equation (8.9),
(Note that we should “round up” since n will ...