Question

In the U.S. court​ system, a defendant is assumed innocent until proven guilty. Suppose that you regard a court trial as a hypothesis test with null and alternative hypotheses

Ho: Defendant is innocent

Ha​: Defendant is guilty.

a. Explain the meaning of a Type I error.

b. Explain the meaning of a Type II error.

c. If you were the​ defendant, would you want Alpha to be large or​ small? Explain your answer.

d. If you were the prosecuting​ attorney, would you want β to be large or​ small? Explain your answer.

e. What are the consequences to the court system if you make Alpha equals=​0? Βeta equals=​0?

Answer 1

Given,

H0: Defendant is Innocent

Ha: Defendant is Guilty

Answer a:
When one rejects the null hypothesis when it it true, then this error is called Type I Error.It is generally represented as in Hypothesis Testing

In this case, Type I Error is interpreted as Defendant is deemed Guilty when the actual fact is he/she is Innocent.

Answer b:

When one accepts the null hypothesis when it it false, then this error is called Type II Error. It is generally represented as in Hypothesis Testing

In this case, Type II Error is interpreted as Defendant is deemed Innocent when the actual fact is he/she is Guilty.

Answer c:

If I was the defendant, I would want to be as small as possible.

Because if is large then the probability of committing a Type I Error increases, that is, Defendant is deemed Guilty when the actual fact is, he is Innocent. This would improve my chances of being treated as a guilty person and not as Innocent. So, I would want to be as small as possible

Answer d:
If I were the prosecuting attorney I would want to be as small as possible.

Because if is large, then probability of committing a Type II Error increases, that is, Defendant is deemed Innocent when the actual fact is he/she is Guilty. It would improve the chances of the Defendant not getting the required punishment for the crime he committed. So, I would want to be as small as possible.

Answer e:
If = 0, it means that Probability of committing a Type I Error is 0, that means, the null hypothesis is accepted when it is actually true. Further it means that Defendant is Innocent and is let off by the court system and hence, the right judgement is given by the court system.

If = 0, it means that Probability of committing a Type II Error is 0, that means, the null hypothesis is rejected when it is actually false. Further it means that Defendant is Guilty and is convicted in the court of law and hence the right judgement is given by the court system.