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

$H_0:$Defendant is innocent

$H_a:$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.

e. What are the consequences to the court system if you make $\alpha =0?\beta =0?$

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

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

This is a type - I mistake.

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

This is the Il error type.

The type-I error probability $\alpha$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 true$H_0$being rejected.

The prosecution attorney would like the type - Il error ,$\beta$to be modest since rejecting the incorrect null hypothesis is crucial to him. Naturally, he will endeavor to reduce the likelihood of mistaken rejection$H_0$.

$$\begin{gathered} \alpha =0 \\ \text{i.e.,}P(\text{Type}-\text{I error})=0 \end{gathered}$$

It means that an innocent person is never found guilty because true is never rejected.$H_0$.

localid="1651572469422" $$\begin{gathered} \beta =0 \\ \text{i.e.,}P\text{(Type}-\text{II error})=0 \end{gathered}$$

It indicates that a guilty person is always found guilty since there is no possibility for false evidence to be rejected.localid="1651572456302" $H_0$.