- 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
confidence
interval for a mean , based on the
*t*distribution, is

where ,*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

since the above relation can be written

For the inequality 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
probability of

- Example 12.12 on page 449