Question

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

Null: Defendant is innocent

Alternative: 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 beta to be large or small? Explain your answer.

Answer 1

(a)

H0: Null Hypothesis Defendant is guilty

HA: Alternative Hypothesis: HA: Defendant is not guilty

Type I Error : Rejection of a true null hypothesis.

Suppose in reality the defendant is guilty. But, the judge wrongly concludes that the defendant is not guilty. Type I error is committed in this situation.

(b)

Type II Error : Failure to reject of a false null hypothesis.

Suppose in reality the defendant is not guilty. But, the judge wrongly concludes that the defendant is guilty. Type II error is committed in this situation.

(c)

If I were the defendant, I want alpha to be large, because the probability of making a Type I error is alpha. So, If alpha is large, there is more probability of the judge making a mistake of wrongly concluding that the defendant is not guilty

(d)

If I were the prosecuting attorney, I want beta to be large, because the probability of making a Type II error is beta. So, If beta is large, there is more probability of the judge making a mistake of wrongly concluding that the defendant is guilty