Standard error of a defect rate

Question

In an inspection of n = 625 parts, a fraction \hat{p} = 0.20 were defective. What is the standard error of the sample defect rate?

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The defect rate is a proportion, an average of "defective / not defective" flags, so it carries a standard error: 	ext{SE} = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}. With \hat{p} = 0.20 and n = 625: 	ext{SE} = \sqrt{\frac{0.20 	imes 0.80}{625}} = \sqrt{\frac{0.16}{625}} = \sqrt{0.000256} = 0.016. So the measured 20\% defect rate is precise to about 1.6 percentage points. The large sample of 625 keeps the standard error small even though defects are fairly common. Takeaway. A proportion's standard error is \sqrt{\hat{p}(1-\hat{p})/n}: a big sample (625) pins a 20\% rate down to about \pm 1.6 po…

Standard error of a defect rate

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