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Math Help - sample size?

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    sample size?

    In sampling without replacement from a population of 900, itís 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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    Quote Originally Posted by het_490@yahoo.com View Post
    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?
    For a small population: \sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} \sqrt{\frac{N - n}{N -1}}
    where \sigma is the population standard deviation, N is the population size and n is the sample size.

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


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


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

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