6.4 What does a hypothesis test do?

• What are the two possible outcomes of a hypothesis test?
• What are the four-possible combinations of (a) hypothesis test result; and (b) state of the world?
• Does a hypothesis test always have to report a result that is consistent with the state of the world? What does it mean if it does, and what does it mean if it does not.
• What if you made up your own testing framework, called the {Your Last Name’s} Groundhog test. Which is literally a groundhog looking to see its shadow. Because you made the test, suppose that you know that it is totally random whether a groundhog sees its shadow. How useful would this test be at separating states of the world?
  
• What guarantee do you get if you follow the decision rules properly?
• Why do we standardize the mean to create a test statistic?

\[ t = \frac{ \overline{X}_n - \mu}{\sqrt{\frac{s^2}{n}}} \]