Question 513336: Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 95 bank accounts, we want to take a random sample of seven accounts in order to learn about the population. How many different random samples of seven accounts are possible?
Answer by drcole(72)   (Show Source):
You can put this solution on YOUR website! In general, you use combinations to determine the number of ways you can select a sample of size n from a population of size N. The formula for the number of such combinations is:
N choose n = N! / (n!)((N - n)!)
where N! (spoken "N factorial") equals N(N - 1)(N - 2)***(3)(2)(1) (for example 7! = (7)(6)(5)(4)(3)(2)(1) = 5040).
In this problem, our population size is N = 95 back accounts, and our sample size is n = 7 bank acccounts. So we want to find:
95 choose 7 = 95! / (7!)((95 - 7)!) = 95! / (7!)(88!) = 11,050,084,695 possible random samples
Many scientific, graphing, and statistical calculators will compute this for you --- look for something that looks like nCk (here we are using N in place of n and n in place of k, so for this problem you want to compute 95C7). You don't have to actually compute 95!, and I wouldn't advise it.
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