Confidence and margin of error in samples

#1
Hi
Forgive me, but my statistics knowledge is terrible having chosen mechanics to go alongside pure mathematics at school, but I have now come across a work problem I need help with.

It is to do with sampling and how to assess either a sample size or a 'confidence' given a sample size. I put 'confidence' in quotes as I know it has specific meaning and I'm probably using the lay man's interpretation.

Here is the scenario.

In a country, a government body issues X new regulations in a month on any of the 22 working days in the month.
I have a person reviewing the government web site to identify when a regulation is issued and then record it in my register of regulations.
At the end of a quarter I need to take a sample to see if the person has been doing their job and to give me a level of assurance (not using confidence) that they have captured all regulations.

Since I don't know how many regulations were actually issued, I can only sample based on a number of days. The data I will have will be:
- number of days sampled
- total number of days in the period being sampled
- number of regulations issued on the days being sampled
- number of regulations correctly captured

It is a simple yes/no answer for each regulation, that being "have they captured the regulation or not"

So what I want to know is (and this is where my language may be wrong) how do I calculate the sample size so that if 100% of the regulations in my sample have been correctly captured then I have a (say) 90% assurance that all regulations have been captured.

I hope that makes sense, but ask away if you need clarification.
 
#2
I suspect that the question as you ask it isn't possible. I'm not entirely sure I understand your situation but I think that is related to something like this -
Imagine you have a bucket with 1000 marbles in it. Probably the bucket contains 1000 green marbles, but there is a small probability p, that there is one red marble in the bucket contaminating the other 999 green ones. You now take a sample of some particular number of marbles from your bucket and they are all green. What is the probability that you have started with a pure bucket with 1000 greens. This problem can be solved only if you know the value of p, the likelihood of a red marble contaminating the bucket. So unless you know p, you cannot work out how many to take to be 90% sure that you have the pure green bucket.
However, there is a related matter which may be of use to you. In quality control there is a "Rule of three". It says that to be 95% sure that the failure rate is less than 1 in N, you need to have 3N occurrences without a failure. So, if you want to be 95% sure that less than 1 milk carton in 1000 leaks, then you need to inspect 3000 cartons without a single leak. https://en.wikipedia.org/wiki/Rule_of_three_(statistics)
If you want to be 95% sure that less than 1 regulation in 100 is incorrectly captured, you will need to inspect 300 without failure.
You mentioned 90% assured. For this you can reduce the "rule of three" to the "rule of 2.3" so to be 90% sure that the failure rate is less than 1 in 1000, you will need to inspect 2.3x1000=2300 without failure.