My Math Forum Sample Size and Margin of Error

 Probability and Statistics Basic Probability and Statistics Math Forum

 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 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?
 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.... Thanks from Scully 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:
 Originally Posted by 123qwerty 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?

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
Quote:
 Originally Posted by Scully 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.

 Tags error, margin, sample, size

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Engr Faisal hbaib Advanced Statistics 0 November 23rd, 2013 06:25 PM Aqil Advanced Statistics 0 March 21st, 2012 01:28 AM jskrzy Algebra 1 November 16th, 2011 04:17 PM waza086 Algebra 0 March 21st, 2010 02:54 AM symmetry Advanced Statistics 0 March 30th, 2007 04:09 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top