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## Interval Estimate with Specified Precision

• 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

Next: Output Analysis for Steady-State Up: Output Analysis for Terminating Previous: Interval Estimate for a
Meng Xiannong 2002-10-18