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Question 344:



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When you test a single mean you are usually testing to see if it is significantly different than 0 or some other number. When you test two means you want to know if each mean is different than each other and have to take into account the variability (standard deviation) of both samples when testing the means.

When you use the z-score you are assuming that the data comes from a roughly normally distributed (bell-shape) population and your sample size is sufficiently large (usually at least 30, but closer to 100) to use the z-test.  If you are testing two means you also are assuming their variances are not very different than each other (homogeneity of variance).

The sample standard deviation can be used, and is almost always used in place of the population SD b/c the population SD is not known. It is needed for example in the t-test and can be used in the z-test if the sample is large(>30), so the estimate is more accurate.

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