In sampling without replacement from a population of 900, it’s found that the standard error of the mean, σx, is only two-thirds as large as it would have been if the population were infinite in size. That is the approximate sample size?

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- Feb 14th 2008, 05:55 AMhet_490@yahoo.comsample size?
In sampling without replacement from a population of 900, it’s found that the standard error of the mean, σx, is only two-thirds as large as it would have been if the population were infinite in size. That is the approximate sample size?

- Feb 15th 2008, 12:33 AMmr fantastic
For a small population: $\displaystyle \sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} \sqrt{\frac{N - n}{N -1}}$

where $\displaystyle \sigma$ is the population standard deviation, N is the population size and n is the sample size.

$\displaystyle \sqrt{\frac{N - n}{N -1}}$ is the*finite population correction factor*.

For a large population: $\displaystyle \sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}}$

The given value of the finite population correction factor is $\displaystyle \frac{2}{3}$ and you're also given N = 900:

$\displaystyle \sqrt{\frac{900 - n}{900 -1}} = \frac{2}{3} \, \Rightarrow \, n \approx 500$.