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When you perform a hypothesis test of a single population mean using a Student's t-distribution (often called a t-test), there are fundamental assumptions that need

When you perform a hypothesis test of a single population mean using a Student's t-distribution (often called a t-test), there are fundamental assumptions that need to be met in order for the test to work properly. Your data should be a simple random sample that comes from a population that is approximately normally distributed. You use the sample standard deviation to approximate the population standard deviation. (Note that if the sample size is sufficiently large, a t-test will work even if the population is not approximately normally distributed)

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