Previous section discusses for a given set of replications to
calcualte the confidence interval and error. Sometimes we need to do
the inverse, given a level of error and confidence, how many
replications are needed?
The half-length (h.i.) of a
interval for a mean , based on the t distribution, is
, S is the sample
standard deviation, R is the number of replications.
Assume an error criterion is specified with a
confidence level , it is desired that a sufficiently large
sample size R be taken such that
Since we have the relation (*), the desired the error control
condition can be written as
Solve the above relation, we have
the above relation can be written
with standard normal distribution holds.
This says we need to run that many (R) replications to satisfy
the error requirement.
The true value of is in the following range with