Interpret the key results for Sample Size for Tolerance Intervals

Complete the following steps to interpret Sample Size for Tolerance Intervals. Key output includes the sample size, the margin of error, and the confidence levels and achieved confidence levels.

In This Topic

Step 1: Examine the calculated sample sizes
Step 2: Examine the calculated maximum acceptable percentages of population for interval

Step 1: Examine the calculated sample sizes

If you specify one or more values for the maximum acceptable percentages of the population in the interval, Minitab calculates the sample sizes that are required to achieve those percentages.

A more precise tolerance interval is more useful and more informative, but smaller margins of error (calculated as maximum percentage of population in interval − minimum percentage of population in interval) require larger sample sizes. 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.

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:

Maximum acceptable percentage of population in interval (P*): The percentage of the population greater than the desired p that might be included in the interval.
Probability the population coverage exceeds p*: The probability that the interval contains more of the population than p*.; Common values for the margin of error probability include 0.01, 0.05, and 0.1. Larger values for the margin of error probability can result in a tolerance interval that covers a much larger percentage of the population than the target, p*.

Method

Confidence level	95%
Minimum percentage of population in interval	90%
Probability the population coverage exceeds p*	0.05

Sample size for 95% Tolerance Interval

P*	Normal Method	Nonparametric Method	Achieved Confidence	Achieved Error Probability
92.000%	1395	2215	95.0%	0.049

Key Results: Sample Size, Achieved Confidence, Achieved Error Probability

In these results, Minitab calculates the sample sizes required to create a tolerance interval that covers 90% of the population. With a probability the population coverage exceeds p* of 0.05 (5%) and a p* value of 92%, the sample size for the normal method is 1395. The sample size for the nonparametric method is 2215. For the nonparametric method, Minitab also displays the achieved confidence level and the achieved error probability for the sample size.

Together, these statistics indicate that there is only a 5% chance that your interval will include 92% or more of the population.

Step 2: Examine the calculated maximum acceptable percentages of population for interval

If you specify one or more sample sizes, Minitab calculates the maximum acceptable percentages of the population in the interval that you can achieve with those sample sizes. Minitab performs calculations for the normal and the nonparametric method. For calculations for other distributions, use Tolerance Intervals (Nonnormal Distribution).

Increasing the sample size decreases the maximum acceptable percentages of the population in the interval. 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.

Method

Confidence level	95%
Minimum percentage of population in interval	95%
Probability the population coverage exceeds p*	0.05

Maximum Acceptable Percentages of Population for 95% Tolerance Interval

Sample Size	Normal Method	Nonparametric Method	Achieved Confidence	Achieved Error Probability
1000	96.5124%	97.0544%	95.7%	0.050
1500	96.2603%	96.7379%	96.1%	0.050
2000	96.1047%	96.5124%	95.8%	0.050

Key Results: Maximum Acceptable Percentages of Population for Tolerance Interval, Achieved Confidence, Achieved Error Probability

In these results, Minitab calculates the maximum acceptable percentages of the population in the interval that are associated with particular sample sizes for tolerance intervals that cover 95% of the population. With a probability the population coverage exceeds p* of 0.05 (5%), the maximum acceptable percentages of the population in the interval for the normal method is approximately 96.5% when the sample size is 1000. When the sample size is 1500, the maximum acceptable percentages of the population in the interval is approximately 96.26%, and when the sample size is 2000, the maximum acceptable percentages of the population in the interval is approximately 96.1%.

The maximum acceptable percentages of the population in the interval for the nonparametric method is approximately 97.05% when the sample size is 1000. When the sample size is 1500, the maximum acceptable percentages of the population in the interval is approximately 96.74%, and when the sample size is 2000, the maximum acceptable percentages of the population in the interval is approximately 96.5%. For the nonparametric case, Minitab also displays the achieved confidence level and the achieved error probability for the sample size. In there results, the achieved error probability is the same as the target error probability for the specified sample sizes, and the achieved confidence levels are slightly greater than the target confidence levels for the specified sample sizes.