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The percent of population in the interval is the minimum percentage of the population that you want the tolerance interval to include. For example, an engineer wants to know the range that will include 99% of the future product, with 98% confidence. 99% is the percent of population in the tolerance interval. MethodConfidence level98%Percent of population in interval99%

Tolerance intervals are a range of values for a specific quality characteristic of a product that likely covers a specified percentage of future product output. Use the normal method tolerance interval if you can safely assume that your sample comes from a normally distributed population.

The normal probability plot shows that the plotted points form an approximate straight line, which indicates that the data follow a normal distribution. Also, the p-value for the normality test is 0.340, which is greater than the significance level (α = 0.05). Thus, there is not enough evidence to conclude that the data do not follow a normal distribution. The engineer can use the normal method results.

Because data samples are random, it is unlikely that two samples from the same population will yield identical tolerance intervals. But, if you collect many samples, a certain percentage of the resulting tolerance intervals will contain the minimum proportion of the population that you specify.

The mean summarizes the sample values with a single value that represents the center of the data. The mean is the average of the data, which is the sum of all the observations divided by the number of observations.

The normal lower bound is 1085.947, so the engineer is 95% confident that at least 95% of all the light bulbs exceed approximately 1086 hours of burn time. For all the light bulbs, the mean burn time is approximately 1248 hours and the standard deviation is approximately 84.1.

The sample size (N) is the total number of observations in the sample. In this data, the sample size is 400. StatisticsVariableNMeanStDevC14000.6043.671

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A larger standard deviation indicates that your data are spread more widely around the mean and will result in a wider tolerance interval. A smaller standard deviation indicates that your data are distributed more closely around the mean and will result in a narrower tolerance interval.

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For the nonparametric method, Minitab calculates the achieved confidence level. This is the exact confidence level obtained from your sample. It will generally be greater than or equal to the target confidence level, unless your sample size is too small.

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Tolerance intervals are a range of values for a specific quality characteristic of a product that likely covers a specified proportion of future product output. If you cannot safely assume that your sample comes from a normally distribution population, you must use the nonparametric method tolerance interval.

The normal method is not robust to severe departures from normality. If you are unsure of the parent distribution, or you know that the parent distribution is not normal, then use the nonparametric method.

The nonparametric method requires only that the data are continuous. However, the nonparametric method requires large sample sizes for the results to be accurate. If your sample size is not large enough, the nonparametric interval is a non-informative interval that ranges from negative infinity to infinity. In this case, Minitab displays a finite interval based on the range of your data. As a result, the achieved confidence level is much lower than the target confidence level.

You can specify the confidence level for the analysis in the Options dialog box. Minitab displays the target confidence level in the Methods table. By default, the confidence level is 95%. For the nonparametric method, Minitab calculates the achieved confidence level. The achieved confidence level is the exact confidence level that Minitab calculates. The achieved confidence level is usually greater than or equal to the target confidence level, unless your sample size is too small.

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The confidence level is the likelihood that the tolerance interval actually includes the minimum percentage. For example, an engineer wants to know the range within which 99% of the future product will fall, with 98% confidence. 98% is the confidence level for the tolerance interval. MethodConfidence level98%Percent of population in interval99%

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If your data follow a normal distribution, then the normal method is more precise and economical than the nonparametric method. The normal method allows you to achieve smaller margins of error with fewer observations.

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