This week we are discussing hypothesis testing. Hypothesis tests can be confusing if you have not seen them before, but they have a lot in common with a criminal trial.  Basically, in a criminal trial there is a defendant who is alleged to have committed a crime and a prosecutor who represents the People or State whose duty is to prove the guilt of the person charged. Note that in the U.S., a defendant is assumed to be innocent until proven guilty.  This is not true in all countries!

Please answer the following questions:

1) What would be the null and alternative hypothesis in a criminal trial?

2) What is the 'burden of proof' for the prosecutor in a criminal trial?  How is this related to an 'alpha' value in hypothesis testing?

3) Why is the burden of proof not 'beyond all doubt whatsoever under any circumstances possible"?  Is it theoretically possible to prove someone guilty100% no doubt at all?

4) Read about Type I and Type II error.  After a conclusion is made in a criminal trial, what would be Type I and Type II results?  Which is preferable in our legal system?

5) Finally, in our legal system, is a person acquitted of the charges found 'innocent' or found 'not guilty'?  What is the difference and how does this compare to the general conclusions in a hypothesis test?