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The One-Sample Z-Procedure is used to learn about the mean of a population. Using these procedures, you can calculate a confidence interval or test a hypothesis regarding μ. In order to use these procedures, the following assumptions must be met:
These assumptions are in addition to the usual two assumptions that the sample is representative of the target population and that the sample values are independent.
If any of these assumptions are not met, then this is not the appropriate procedure to use. Note that the actual first assumption is that the sample means are Normally distributed. However, since you have but one sample mean, this assumption cannot be directly assessed. An equivalent assumption is that the data are from a Normal distribution.
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