We assume that the standard deviation of the distribution is known, and compute
a confidence interval using a point estimator for the mean , such as
as follows:
Note: The larger the sample size, the tighter the limits (the smaller the confidence interval).
We make use of this principle if we seek to find a confidence interval of fixed
size. For example, suppose that you want to find a confidence interval of at
most size 1 ounce about the quantity of beer in a cup. You may believe that the
18 ounce beer that's promised is actually no more than 17 ounces (and more than
likely 16 ounces). So you seek to demonstrate this fact with a significance
level of . We can solve to make the bounds around
,
equal W in size (in the beer example we'd set W to 1). To do this, solve
for n, from which we get
This tells us how to select our sample size so as to guarantee a given sized
confidence interval.