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March 29th, 2016, 06:12 PM   #1
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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 non-acceptable defects. Non-acceptable defects are sent back to assembly line for re-work. Inspector finds 90% of machine parts, 20 parts, have to be sent back for re-work.

Does this mean that 85% - 95% of the machine parts with defects in the population of 500 have to be sent back for re-work?
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March 30th, 2016, 09:31 AM   #2
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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....
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Last edited by 123qwerty; March 30th, 2016 at 09:33 AM.
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March 30th, 2016, 06:36 PM   #3
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Quote:
Originally Posted by 123qwerty View Post
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....
Thanks 123qwerty.

If the sample size is 22, then is the population size 218 or 500?
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March 30th, 2016, 06:49 PM   #4
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Originally Posted by Scully View Post
Thanks 123qwerty.

If the sample size is 22, then is the population size 218 or 500?
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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