Sample Tests for a Population Mean: Key Takeaways

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There are two formulas for the test statistic in testing hypotheses about a population mean with small samples. One test statistic follows the standard normal distribution, the other Student's $t$ -distribution.
The population standard deviation is used if it is known, otherwise the sample standard deviation is used.
Either five-step procedure, critical value or $p$ -value approach, is used with either test statistic.