# Determining population defect rate from sample defect rate

#### unueco

##### Registered
I have what seems like it should be a simple question --

A sample of 29% of a lot is taken. 3.7% are found to be defective. What is the likely % of defective units in the population?

This seems like the sort of problem I solved with ease during my college years. But that was back when dinosaurs roamed the earth. So.....alzhemiers and all that.

If we assume a homogenous distribution of defects, it would seem the answrer is 3.7%. But, I seem to recall that defects aren't distributed uniformly; the hypergeometric distribution is used.

Anyway, any assistance and/or refresher tutorial would be appreciated.

Thank you!

#### Miner

##### Forum Moderator
I think you are looking for the confidence interval for a proportion. There are online calculators that you can use to generate a confidence interval for a desired confidence level.

#### unueco

##### Registered

....confidence interval for a proportion..
So it seems you're saying that I am essentially looking at a proportion--

2:53 as is X:400

....and then compute a confidence interval around this proportion.

Do I understand you correctly?

It would also seem that this verifies the assumption that defects are distributed homogeneously throughout the lot.

#### Miner

##### Forum Moderator
That is correct.

It is not so much whether the defects are distributed homogeneously, but when a particular distribution applies. The hypergeometric distribution is used when you are repeatedly sampling without replacing the units sampled because you are gradually changing the proportion of defectives with each repeat sample. The binomial distribution is used when you do replace the samples. However, there are two things to consider:
• When the sample size is a small percent of the population, the distributions are essentially the same
• When you are only taking a single sample from a lot, you are no longer sampling repeatedly, so binomial applies.