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- Tolerance_interval abstract "A tolerance interval is a statistical interval within which, with some confidence level, a specified proportion of a sampled population falls. "More specifically, a 100×p%/100×(1−α) tolerance interval provides limits within which at least a certain proportion (p) of the population falls with a given level of confidence (1−α)." "A (p, 1−α) tolerance interval (TI) based on a sample is constructed so that it would include at least a proportion p of the sampled population with confidence 1−α; such a TI is usually referred to as p-content − (1−α) coverage TI." "A (p, 1−α) upper tolerance limit (TL) is simply an 1−α upper confidence limit for the 100 p percentile of the population."A tolerance interval can be seen as a statistical version of a probability interval. "In the parameters-known case, a 95% tolerance interval and a 95% prediction interval are the same." If we knew a population's exact parameters, we would be able to compute a range within which a certain proportion of the population falls. For example, if we know a population is normally distributed with mean and standard deviation , then the interval includes 95% of the population (1.96 is the z-score for 95% coverage of a normally distributed population).However, if we have only a sample from the population, we know only the sample mean and sample standard deviation , which are only estimates of the true parameters. In that case, will not necessarily include 95% of the population, due to variance in these estimates. A tolerance interval bounds this variance by introducing a confidence level , which is the confidence with which this interval actually includes the specified proportion of the population. For a normally distributed population, a z-score can be transformed into a "k factor" or tolerance factor for a given via lookup tables or several approximation formulas. "As the degrees of freedom approach infinity, the prediction and tolerance intervals become equal."".
- Tolerance_interval wikiPageExternalLink 0470380268.pdf.
- Tolerance_interval wikiPageID "833690".
- Tolerance_interval wikiPageRevisionID "605571605".
- Tolerance_interval hasPhotoCollection Tolerance_interval.
- Tolerance_interval subject Category:Engineering_concepts.
- Tolerance_interval subject Category:Prediction.
- Tolerance_interval subject Category:Statistical_forecasting.
- Tolerance_interval subject Category:Statistical_inference.
- Tolerance_interval subject Category:Statistical_intervals.
- Tolerance_interval subject Category:Statistical_terminology.
- Tolerance_interval type Abstraction100002137.
- Tolerance_interval type Cognition100023271.
- Tolerance_interval type Concept105835747.
- Tolerance_interval type Content105809192.
- Tolerance_interval type EngineeringConcepts.
- Tolerance_interval type Idea105833840.
- Tolerance_interval type Measure100033615.
- Tolerance_interval type PsychologicalFeature100023100.
- Tolerance_interval type StatisticalIntervals.
- Tolerance_interval type TimeInterval115269513.
- Tolerance_interval comment "A tolerance interval is a statistical interval within which, with some confidence level, a specified proportion of a sampled population falls.".
- Tolerance_interval label "Tolerance interval".
- Tolerance_interval sameAs m.03fmgh.
- Tolerance_interval sameAs Q7814221.
- Tolerance_interval sameAs Q7814221.
- Tolerance_interval sameAs Tolerance_interval.
- Tolerance_interval wasDerivedFrom Tolerance_interval?oldid=605571605.
- Tolerance_interval isPrimaryTopicOf Tolerance_interval.