Overview of Confidence Intervals (1 of 2)
Before a simple research question such as "What is the
mean number
of digits that can be remembered?" can be answered, it is necessary to
specify the
population of people to which it is addressed.
The researcher could be interested in, for example, adults over the age of 18,
all people regardless of age, or students attending high school. For the present
example, assume the researcher is interested in students attending high school.
Once
the population is specified, the next step is to take a
random
sample from it. In this example, let's say that a sample of 10 students
were drawn and each student's memory tested. The way to estimate the mean of
all high school students would be to compute the mean of the 10 students in
the sample. Indeed, the
sample mean is an
unbiased estimate
of μ, the
population mean. But it will certainly
not be a perfect estimate. By chance it is bound to be at least either a little
bit too high or a little bit too low (or, perhaps, much too high or much too
low).
For the estimate of μ to be of value,
one must have some idea of how precise it is. That is, how close to μ is
the estimate likely to be?