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I have population size of $2000$. I used Cochran's formula to determine sample size which is $$\text{Sample Size} = \frac{n}{1 + (n/\text{population})}$$ in which $n$ is equal to $Z * Z [P (1-P)/(D*D)]$ (using a 95% confidence and $5\%$ margin of error and $p = 0.5$) which gives me sample size $323$.

My question: is $323$ the minimum sample size? Can I take larger sample?

If I have population size $800$ and using the same formula again I get sample size $18$ (using $10\%$ margin of error and $95\%$ confidence, $p=95\%$) then isn't the sample size too small to carry the hypothesis test?

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    $\begingroup$ Is this for a power analysis? What test are you going to run? What is the magnitude of the effect that you want to be able to differentiate from 0 (or whatever your null is)? $\endgroup$ – gung - Reinstate Monica Dec 12 '12 at 15:34
  • $\begingroup$ For the first example which i have stated, i wanted to test the adoption of particular programme by the population, my null hyp h0: p=0.5 and for the sceond example i wanted to test accuracy of a process adopted by the population so my null hyp: p=.95 $\endgroup$ – priyasaha10 Dec 14 '12 at 8:09
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  1. You can always take a larger sample.
  2. The "general" rule of thumb is that you want at least 30 samples to be statistically reasonable, so yes a sample size of 18 is likely to be too small with a population of 800.
  3. Your calculation is missing something as you should get a sample size around 89 for a population of 800 with 10% precision.

Yamane (1967) has a simplified formula for calculating sample size. A 95% confidence level and P = .05 are assumed.

$n=N/(1+N(e^2))$

n=800/(1+800(.10^2)) = 88.88
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