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The Complete Idiot's Guide to Statistics, 2nd Edition by Robert Donnelly

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Confidence Intervals for the Mean with Small Samples

So far, this entire chapter has dealt with the case where n ≥ 30. I’m sure you are now wondering about how to construct a confidence interval when our sample size is less than 30. Well, as with many things in life, it depends.
 
With a small sample size, we lose the use of our faithful friend, the central limit theorem, and we need to assume that the population is normally (or approximately) distributed for all cases. The first case that we’ll examine is when we know σ, the population standard deviation.

When σ Is Known

When σ is known, the procedure reverts back to the large sample size case. We can do this because we are now assuming the population is normally distributed. Let’s construct ...

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