Regarding the sample data (problem #2) for which you calculated the 99th percent

Question

Regarding the sample data (problem #2) for which you calculated the 99th percentile statistic, management isn't convinced because you haven't reported statistical confidence. What happens when you calculate a 95% confidence for the upper tolerance limit of the 99th percentile statistic?

Select one:

a. The value becomes lower and it is apparent that compliance will be easily obtained.

b. The value becomes a bit higher, but we still have nothing to worry about because it isn't above the PEL.

#1 Problem

A coworker comes to you with personal air sample results. He shows you that the geometric mean of the similar exposure group (SEG) is 2.45 PPM with a GSD of 1.25. Since the PEL for this substance is 4 PPM, your coworker is ecstatic that there are no overexposures and there is no chance of an overexposure. Should he be so enthusiastic?

#2 Problem

You look at the exposure data in the sampling problem (#1) and recognize that these values are almost certainly lognormally distributed and that your coworker was correct to calculate a GM and GSD. You are, however, skeptical that the safety department can rest easy so you calculate the 99th percentile decision statistic for these values. What do you tell your coworker?

Select one:

a. You were right! The 99% percentile decision statistic is only 2.45, which is well below the PEL. We have nothing to worry about.

b. Well, I'm sorry to say this, but the 99% percentile decision statistic is 5.1, so we have a lot to be worried about since future air samples could easily be above 4. This is a very dangerous situation and we need to stop production immediately to address this problem.

c. The 99% percentile decision statistic is 4.2, so there is possibility of an overexposure in future personal air sample values. We need to take steps now to reduce the exposures so there is less potential health risk to our employees and lowered overall risk to the company.

d. You were right! The 99% percentile decision statistic is only 2.7, which is well below the PEL. We have nothing to worry about.

1.0 3.9 3.0 2.0 2.0 3.0 3.8 Regarding the sample data (problem #2) for which you calculated the 99th percentile statistic, management isn't convinced because you haven't reported statistical confidence. What happens when you calculate a 95% confidence for the upper tolerance limit of the 99th percentile statistic? Select one: o a. The value becomes lower and it is apparent that compliance will be easily obtained. b. The value becomes a bit higher, but we still have nothing to worry about because it isn't above the PEL O c. The value becomes much higher and we should have a lot of concern about a possible -albeit unlikely- over exposure.

Explanation / Answer

Using the above data we calculate sample mean = 2.67143 and standard deviation = 1.05627

Now X~N( 2.67143 ,1.05627)

P(X<x)=0.99 then we use the following path to find x,

Minitab-calc-Probability Distributions-Normal Distribution-Inverse Cumulative Probability

we get x=5.12868~5.1

Hence

b. Well, I'm sorry to say this, but the 99% percentile decision statistic is 5.1, so we have a lot to be worried about since future air samples could easily be above 4. This is a very dangerous situation and we need to stop production immediately to address this problem.

Problem 1 : He should not be so enthusiastic .

Regarding the sample data (problem #2) if I calculate a 95% confidence for the upper tolerance limit of the 99th percentile statistic,

c. The value becomes much higher and we should have a lot of concern about a possible -albeit unlikely- over exposure.

1.0 3.9 3.0 2.0 2.0 3.0 3.8

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