# Sample size to guarantee I have at least ONE part from the lower 25% of the populatio

#### BobQA

##### New Member
Parts came from supplier with a heat treat process missing. Parts are soft, ranging from 16 to 21, Mean = 18, SD=1.26 (should be Rc 28 or greater)

We need to test parts from the lower range in units to assure our customer if we can use this batch or not. The test is destructive, once tested the part can not be used!

How do I determine what sample size I need to pick for in unit testing to guarantee I have at least ONE part from the lower 25% of the population?

How do I calculate the sample size? What that test plan called?

thanks

#### Dason

##### Ambassador to the humans
Re: Sample size to guarantee I have at least ONE part from the lower 25% of the popul

You can't guarantee it. But you can choose a sample size such that there will be a very high probability of obtaining an element of interest

#### rogojel

##### TS Contributor
Re: Sample size to guarantee I have at least ONE part from the lower 25% of the popul

how about using something like the stratified random sampling? chose a subsample ( not a random pne) from the lower 25% and pick a gew randomly from them?

With random sampling as Dason said there is no guarantee, but you need not do a completely random sampling, right?

#### BobQA

##### New Member
Re: Sample size to guarantee I have at least ONE part from the lower 25% of the popul

Empirically I think about 8 will assure. Guarantee to the 95% CI level is what "guarantee" means.

I remember a long time ago a prof showing how it was done, you break the distribution up into segments and calculate the probability of picking from the segment(s) you are interested in.

I am looking for a reference to the math, or what it is called so I can google it.

You can't guarantee it. But you can choose a sample size such that there will be a very high probability of obtaining an element of interest

#### BobQA

##### New Member
Re: Sample size to guarantee I have at least ONE part from the lower 25% of the popul

Just to end the thread, not as tough as I thought.

Given the distribution of the sample, I know the normal gaussian curve. And that
22% of the population was in the target area. Therefore to resonably assure that I get at least 2 samples in my target area, n=2/.22 or roughly speaking I need to pick at least 9 units for testing.

Of course I am not sure what the CI is for getting at least 1 unit in my target area.

I would be interested if anyone knows that calculation.

Empirically I think about 8 will assure. Guarantee to the 95% CI level is what "guarantee" means.

I remember a long time ago a prof showing how it was done, you break the distribution up into segments and calculate the probability of picking from the segment(s) you are interested in.

I am looking for a reference to the math, or what it is called so I can google it.

#### Dason

##### Ambassador to the humans
Re: Sample size to guarantee I have at least ONE part from the lower 25% of the popul

For a given sample size the number that fall within your target area will follow a binomial distribution. You can explore various sample sizes to see if it's good enough. For example for a sample size of 9 the probability that get at least two people in the target area (given the probability an individual falls in that area is .22) is just 0.6218484

Here is a table for a couple higher sample sizes:
Code:
      Prob Sample Size
0.6815306          10
0.7332552          11
0.7776348          12
0.8153979          13
0.8473077          14
0.8741119          15
0.8965126          16
0.9151500          17
0.9305957          18
0.9433520          19
0.9538547          20

#### BobQA

##### New Member
Re: Sample size to guarantee I have at least ONE part from the lower 25% of the popul

Right you are! Since I need only one in the target area, it rises to ~90%.

Thanks for the pointer to a binomial distribution.

Here's a link to a good binomial calculator:

http://stattrek.com/online-calculator/binomial.aspx

For a given sample size the number that fall within your target area will follow a binomial distribution. You can explore various sample sizes to see if it's good enough. For example for a sample size of 9 the probability that get at least two people in the target area (given the probability an individual falls in that area is .22) is just 0.6218484

Here is a table for a couple higher sample sizes:
Code:
      Prob Sample Size
0.6815306          10
0.7332552          11
0.7776348          12
0.8153979          13
0.8473077          14
0.8741119          15
0.8965126          16
0.9151500          17
0.9305957          18
0.9433520          19
0.9538547          20