Sample Size Experiment Proportion Failure I have N machines and I want to implement an experiment E in them in order to improve their proportion of failures.
However, I’m not sure yet if this experiment E will increase, decrease or do nothing in my proportion of failures.
Therefore, in the beginning I want to implement experiment E in only a sample (of size n) of these N machines in order to compare the proportion of failures of the machines under experiment E and the proportion of failures of the machines which are not under experiment E. After that I’ll decide if should roll out experiment E to my hole population.
What is the best way to define the sample size n?
 A: Well, there are multiple ways to define a sample size.
If you already have a Z-Score, standard deviation, and a margin of error (alpha level), you can use this formula (which uses Z-Score, standard deviation, and error rate):


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*https://www.isixsigma.com/wp-content/uploads/images/stories/migrated/graphics/sampleformula.gif
However, if you are conducting an experiment (as you state) and want to figure out a number, it can be a bit more complex.  Obviously, as you increase the size of your sample, the more accurate your information!  Now before you begin, you want to figure out your population size (or an estimate, if it is incredibly large and not easy to count).  From there, you would want to determine your confidence interval and margin of error (which should add up to 100%, so if your C.I. is .95, your M.E. should be .05!)  
That is the answer in essence, but that really only gives the bare minimum of what you should have for it to be significant and worth your while.  Technically you can make it as large as you want, but in most cases that takes an unreasonable amount of time and doesn't really make a meaningful difference).  There are also many calculators online that can help you determine a sample size (most of which use the information I gave above.)  I will provide a fairly simple one here:


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*https://www.surveymonkey.com/mp/sample-size-calculator/
If you want to read more about selecting a sample size in detail, here is a very nice resource that explains it in great depth (and shows examples!):


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*https://www.isixsigma.com/tools-templates/sampling-data/how-determine-sample-size-determining-sample-size/
Hopefully this answers your question!
