In this lesson, we'll continue our investigation of hypothesis testing. In this case, we'll focus our attention on a hypothesis test for a population mean \(\mu\) for three situations:

• a hypothesis test based on the normal distribution for the mean \(\mu\) for the completely unrealistic situation that the population variance \(\sigma^2\) is known
• a hypothesis test based on the \(t\)-distribution for the mean \(\mu\) for the (much more) realistic situation that the population variance \(\sigma^2\) is unknown
• a hypothesis test based on the \(t\)-distribution for \(\mu_D\), the mean difference in the responses of two dependent populations