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

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Testing for Differences Between Means with Large Sample Sizes

When the sample sizes from both populations of interest are greater than 30, the central limit theorem allows us to use the normal distribution to approximate the sampling distribution for the difference in means. Let’s demonstrate this technique with the following example.
 
Studies have been done to investigate the effects of stimulation on the brain development of rats. I guess the logic being what’s good for rats can’t be all that bad for us humans. Two samples were randomly selected from the same rat population.
 
The first sample, we’ll call these the “lucky rats” (Population 1), was surrounded with every luxury a rat could imagine. I can envision a country club atmosphere, ...

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