Sample Size for Tolerance Intervals

Calculating Margin of Error - Nonparametric Method

  

Minitab also calculates margins of error using the nonparametric method. The results for the nonparametric method include the following:

·    Achieved confidence: The exact confidence level that is associated with the specified sample size. The achieved confidence is usually greater than or equal to your desired confidence level. However, if your sample size is too small, the achieved confidence can be lower than the desired level.

·    Achieved error probability: The exact margin of error probability that is associated with the specified sample size. The achieved error probability is usually close to your desired level.

Example Output

Method

 

Confidence level                    95%

Percent of population in interval   95%

Margin of error probability        0.05

 

Margin of Error for 95% Tolerance Interval

 

Sample   Normal  Nonparametric    Achieved  Achieved Error

  Size   Method         Method  Confidence     Probability

    50  4.4015%        4.2846%       72.1%           0.050

   100  3.6914%        4.6435%       96.3%           0.050

 

Achieved confidence and achieved error probability apply only to nonparametric method.

Interpretation

The results show that, with 50 observations, the margin of error for a tolerance interval that is calculated using the nonparametric method is 4.2846%. But notice that the achieved confidence level is only 72.1%. Thus, the interval will include 95% of the population only 72.1% of the time, rather than 95% of the time.

Increasing the sample size to 100 improves the achieved confidence for the nonparametric method to 96.3%, and the margin of error is 4.6435%. In other words, with 100 observations, there is a 5% chance that the tolerance interval will contain 99.6435% or more of the population.