## Sample Tests for a Population Mean

This section talks about using the central limit theorem to test a population mean when the sample size is large. It also addresses how to interpret the test results in the application background. Then, it discusses testing a population mean when the sample size is small, outlines a five-step testing procedure, and illustrates the procedure with an example. Study the example carefully and complete the relevant exercises and applications. Finally, it talks about large sample tests for a population proportion. The critical value and p-value approach are introduced based on a standardized test statistic.

### Small Sample Tests for a Population Mean

#### KEY TAKEAWAYS

• 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.