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March 29th, 2016, 06:12 PM  #1 
Member Joined: May 2015 From: USA Posts: 34 Thanks: 1  Sample Size and Margin of Error
I'm crafting a study and am not sure if the below hypothetical approach is right: A robotic eye scans man made machine parts for defects. 500 machine parts were made in Feb 2016. A human inspector takes a sample size of 218 and manually inspects for defects. Inspector finds 10% of machine parts have defects, so we can be 95% certain that 5 – 15% of machine parts in population of 500 have defects. This 10% of 218, 22 machine parts, are inspected by the same inspector for acceptable or nonacceptable defects. Nonacceptable defects are sent back to assembly line for rework. Inspector finds 90% of machine parts, 20 parts, have to be sent back for rework. Does this mean that 85%  95% of the machine parts with defects in the population of 500 have to be sent back for rework? 
March 30th, 2016, 09:31 AM  #2 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics 
Sample size = 22 Sample proportion = 0.9 Thus a 95% CI would be $\displaystyle 0.9 \pm 1.96 \sqrt{\frac{0.9\times 0.1}{22}} \approx (0.77, 1)$ Because the the sample size is small, the estimated variance is quite large.... Last edited by 123qwerty; March 30th, 2016 at 09:33 AM. 
March 30th, 2016, 06:36 PM  #3  
Member Joined: May 2015 From: USA Posts: 34 Thanks: 1  Quote:
If the sample size is 22, then is the population size 218 or 500?  
March 30th, 2016, 06:49 PM  #4 
Senior Member Joined: Dec 2012 From: Hong Kong Posts: 853 Thanks: 311 Math Focus: Stochastic processes, statistical inference, data mining, computational linguistics  The population size is the number of parts with defects in the population of 500. The CI doesn't depend on population size, thankfully, so it doesn't really matter that we don't know how large the population is.


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error, margin, sample, size 
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