In the US court system, a defendant is assumed innocent until proven guilty. Suppose that you regard a court system as a hypothesis test with these null and alternative hypotheses: H0: Defendant is innocent Ha: Defendant is guilty There are 2 possible decisions regarding H0 and 2 possible truths as to the innocence or guilt of the defendant, making 4 possible combinations. What are those 4 combinations? Identify the two correct decisions.

A test hypothesis by definition is a test based on probabilities, therefore it always be possible to make errors when decision is made. According to that we always have 4 possibilities, two right and to wrong (4 possiblities)

For instance in our particular case

H₀ = Defendant is innocent Hₐ = defendant is guilty

If we arrive to conclusion that H₀ is right, and he is really innocent we took a correct decision, And the result will be correct; if we take the decision of reject H₀ when the defendant is guilty again we took the right decision. These are the two correct decision in that case.

On the other hand what happens if we take the decision of rejecting H₀ (accepting Hₐ ) and the defendant is innocent, we are sending the defendant to jail and he is innocente (we are making I type error) and the defendant will pay for it. Finally if we accept H₀ and this decision is not right we will make the defendant be free and he is really guilty