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A one-sample t test is a hypothesis test for determining whether the mean of a population is different from some known (test) value. The researcher begins by selecting a sample of observations from the population of interest and estimates the population mean by calculating the mean of the sample. The researcher then compares this sample mean with the test value of interest via the formula

where is the sample mean, μ is the test value, s is the sample standard deviation, and n is the sample size. This t value can then be used to determine the likelihood that any difference between the sample mean and the test value is real versus a result of chance.

For example, a researcher studying the better-than-average effect might be ...

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