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Guilty or Innocent? 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

H0: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 to be large or small? Explain your answer.

d. If you were the prosecuting attorney, would you wantto be large or small? Explain your answer.

e. What are the consequences to the court system if you make =0?=0?

Short Answer

Expert verified

The explanation for each part has been explained.

Step by step solution

01

Part (a) Step 1. Given information.  

Suppose that you regard a court trial as a hypothesis test with null and alternative hypotheses .

02

Part (a) Step 2. Explanation.

When the defendant is infect, it is assumed that he or she is guilty.

This is a type - I mistake.

03

Part (b) Step 1. Explanation.

When the defendant infects, it is determined that he or she is not guilty.

This is the Il error type.

04

Part (c) Step 1. Explanation.

The type-I error probability would be very low for a defendant, because non-rejection of the true null hypothesis is critical to him. Naturally, he will want to reduce the chances of trueH0being rejected.

05

Part (d) Step 1. Explanation.

The prosecution attorney would like the type - Il error ,to be modest since rejecting the incorrect null hypothesis is crucial to him. Naturally, he will endeavor to reduce the likelihood of mistaken rejectionH0.

06

Part (e) Step 1. Explanation.

=0i.e.,P(TypeI error)=0

It means that an innocent person is never found guilty because true is never rejected.H0.

localid="1651572469422" =0i.e.,P(TypeII error)=0

It indicates that a guilty person is always found guilty since there is no possibility for false evidence to be rejected.localid="1651572456302" H0.

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