CHAPTER 7
ESTIMATION OF POPULATION MEANS:
CONFIDENCE INTERVALS
We consider first a very simple research situation in which we wish to estimate a
population mean p. Pediatricians have included a new substance in the diet of infants.
They give the new diet to a sample of 16 infants and measure their gains in weight
over a 1-month period. The arithmetic mean of the 16 gains in weight is x = 311.9 g.
These specific 16 observations are from a sample and are not the population that
we are studying. That population consists of the infants from which the pediatricians
took their sample in performing the study, and we wish to estimate p, the population
mean weight gain. The target population consists of similar infants who may receive
the new diet in the future.
The point estimate (i.e., an estimate consisting of a single number) for the popu-
lation mean p is the sample mean, or 3 11.9 g. By now, however, enough has been
discussed about sampling variation to make clear that p is not exactly 3 11.9 g, and
we wish to get some idea of what p may reasonably be expected to be. To fill this
need, we compute a confidence interval for p; the term confidence interval will be
defined after the example is worked out.
In Section 7.1 we present an example of computing a confidence interval for a
single mean when the population standard deviation, 0, is known. We also give a
definition of confidence intervals and discuss the choice of the confidence level. In
Basic Statistics: A Primer for the Biomedical Sciences, Fourth Edition.
By Olive Jean Dunn and Virginia A. Clark
Copyright @ 2009 John Wiley & Sons, Inc.79