# Thread: Sample size | Johnson SB distribution

1. ## Sample size | Johnson SB distribution

I have some statistical notions but from one day to the other i was asked to do an analysis that i hope you guys can help me with, since i have no idea how i will be able to do it.

I have data from the last 5 years of a chemical company. This company receives a material from their suppliers and to test if it's acceptable or not they do a density test on this material. They receive it several times a day and they test every single delivery so I have lots of data (from the results of the density test). I have put this data into excel and it seems that it follows a johnson Sb distribution, negatively skewed.

What they asked me to do was, "since there are lots of costs associated with the density test we want to determine the sample size that would give us 95% confidence that average of the test results will be between x and y (error)."
If the distribution was normal i think it would be easy but since it is negatively skewed i'm kind of stuck on this. What steps should i take? Can I turn it into a Normal distribution?

Thank you very much

2. ## Re: Sample size | Johnson SB distribution

Once you take a large enough sample the distribution of the sample mean will be approximately normal. So you could do the calculations the same way you would if you assumed the distribution was normal and check the sample size you get from that to see if it seems large enough for the central limit theorem to kick in.

Alternatively you could just bootstrap the sampling distribution of the sample mean for various values of n until you find one that meets your requirement.

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