# Testing is a sample has been rigged??

#### Andy Carr

##### New Member
Hello All,

This is my first post so please be gentle, I did applied stats 22 years ago as part of my Physics degree but that was, well, 22 years ago! I know the answer to this should be fairly simple but just cannot kick start the brain.

I have a full Population of data that is 3161 large. Of these 539 have a particular undesirable attribute, so 17% of the data have that attribute.

However, a sample of 101 has been MANUALLY (theoretically random, but I suspect not) taken from the population. Only 3 in that sample have been found to have that undesirable attribute. (3%)

MY question is: what is the confidence that the Sample is not Random and has been fixed to avoid undesirable outcomes?

I can follow the Maths if spelt out, and should be able to work out the rest of what I have to do from that point on, and apply it to other samples.

Can you help?

Many thanks

Andy

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#### Miner

##### TS Contributor
You could perform a 1-proportion test against a standard of 0.17. If significant, it will tell you the probability that the sample came from a population with a proportion of 0.17. It does not, however, prove that the sample was taken in a particular manner (i.e., nonrandom). It just suggests that it is unlikely that it came from the same population.

#### hlsmith

##### Omega Contributor
Another potential option:

I know I will mess up this description, but you could replicate the population and take 10,000 or so random samples out of it (of the sample size you are interested in) and see how many (percentage) have the characteristics or worse you are concerned about.

This would likely take a little programming.