# Margin of error for tolerance intervals

A more precise tolerance interval is more useful and more informative. If a tolerance interval is not sufficiently precise, it can be too wide and include a much larger percentage of the population than you specify. You can use Stat > Power and Sample Size > Sample Size for Tolerance Intervals to help you determine the precision of your tolerance intervals.

Suppose that p% is the targeted minimum percentage of the population for a tolerance interval. The following statistics define the precision of the tolerance interval:

Margin of error
The margin of error, m%, measures the additional percentage of the population, beyond the target of p%, that might be included in the interval.
Margin of error probability
The margin of error probability is the probability that the interval will be wider than p% by m% or more. Common values for the margin of error probability include 0.01, 0.05, and 0.1. Larger values can result in a tolerance interval that covers a much larger percentage of the population than the target, p%.

## Example

Suppose you want to calculate a tolerance interval that covers 90% of the population. Using the default margin of error probability of 0.05 (5%), you determine that the margin of error for the interval is 2%. Together, these statistics indicate that there is only a 5% chance that your interval will include 92% or more of the population.

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