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#### noetsi

##### Fortran must die
Sample size can be used for different things. For a given statistical power, to generate a given error rate, to generalize to a population. You need to know what sample size is needed for. My guess is to get a specific error rate, sometimes called the margin of error of the polls

#### Dason

I was tasked with determining a "statistical sample size" for a population of 6070. The purpose is as a spot check with binomial results (is or is not); it is not an acceptance sampling; and I was given no other information (ie. margin of error). There is no baseline or historical data about the population. The only information I have to go on is the size of the population. Is there a statistical method of determining an appropriate sample size when nothing else is known except the size of the population?
In general no but since you're looking at a proportion it's possible here.

#### joeb33050

##### Member
Yes, and the population size has nothing to do with the answer.
We have sample size, expected successes, actual successes, and probability of that difference.

let n = 120, long run Psuccess = PX =.3, expected successes = .3 * 120 = 36 = X
actual success = 40 = x
40/36 = 1.111
Now to an online binomial calculator, example is statrek. Plug in .3, 120 and 40 and get an array of probabilities, one of which is
Cumulative Prob X>x = .1843.
The probability of the long run success probability being > the sample success value is 18.43%.
And we can double that, trust me, to 37%, and say this:
"A binomial distribution with Ps = .3 will have samples of 120 success number between 32 and 40 = +/-11.1%, 1-.37 = 63 percent of the time. So, take a sample of maybe 30, get a ballpark guess at PX-I guessed .3
Put the guess PX, an n and an x into the machine.
Get PX>x.
Change n until you're happy with PX>x
You've solved for n.
Fifteen minutes with an online binomial calculator and you'll become an expert.