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In a population of blue and red ants, I take a random sample of N ants. In that sample, there are 0 red ants and N blue. How do I find the sample variance of the portion of red ants? I don't understand how to go about this. Since I have 0 red ants in my sample, wouldn't the variance just be 0?

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1 Answer 1

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Yes.

I suppose you would have $$SE_{\textrm{red}}^2 = \frac{p_{\textrm{red}}(1-p_{\textrm{red}})}{N} = \frac{0(1)}{N}=0$$

Note that the sample variance of the proportion of blue ants is also zero, since you would have

$$SE_{\textrm{blue}}^2 = \frac{p_{\textrm{blue}}(1-p_{\textrm{blue}})}{N} = \frac{1(0)}{N}=0$$

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