Sample Size Determination
Simple random sampling is generally used to estimate population parameters such as
means, proportions, and variances. When using`x to estimate a population mean, for
example, one also needs to know how close the estimate is to the true population mean.
The error due to sampling variability is given by the standard error of the mean, which is
used to construct a confidence interval on the true population mean. The amount of error
is determined by the sample size and is a crucial issue in sampling.
Thus, a 1 – a probability exists that the value of the sample mean will provide a sampling
error of za/2s/Ön or less. This sampling error is denoted by E. Solving the equation
This sample size will provide a point estimate having a sampling error of E or less at a
confidence level of 100(1 – a) percent.
The next task is to determine the sample size for estimating a population proportion
for attributes data. A point estimate of the population proportion, p, is given by the
sample proportion`p. The standard error of the proportion is
If a good value of`p is not known, use`p = 0.5 since this value provides the largest
sample size recommendation that guarantees the required level of precision.
Suppose a sample from a large finished goods inventory is needed to determine
the proportion of non-conforming product. Historically about a 0.5 percent level of
nonconformance has been observed. A 90 percent confidence level with an allowable
error of 0.25 percent is desired. Thus, E = 0.0025, p-bar = 0.005, and z0.05 = 1.645. The
required sample size is
and thus very small. Discovery sampling tables have been published for selecting the
appropriate sample size.1 An example is shown in the table below. One must know the
population size and critical rate of occurrence and must specify the desired confidence
level. The table gives the probability of finding at least one occurrence in the sample.
Suppose that a nursing manager wants to be 95 percent confident of finding at least
one incident in which nursing personnel have failed to comply with a critical procedure.