In the American justice system, a criminal is presumed innocent until proven guilty, meaning that the prosecution must gather enough evidence to prove that the defendant has actually committed a crime. Suppose a defendant is on trial for robbing a bank. The jury will hear the case and decide on a verdict of guilty or not guilty at the conclusion of the trial.

a. State the null and alternative hypotheses for the defendant. Just use words to describe the hypotheses - no statistical symbols are necessary.

b. Describe how a Type I error could occur during the trial.

c. Describe how a Type II error could occur during the trial.

d. Describe the two ways the correct decision could be made in the trial.

Step-by-step explanation:

Given that in the American justice system, a criminal is presumed innocent until proven guilty, meaning that the prosecution must gather enough evidence to prove that the defendant has actually committed a crime.

H0: The defendent is not guilty

Ha: The defendent is guilty

(Two tailed test)

a) given above

b) Type I error here is false rejection of H0, i. e. charging defendent guilty even though actually he is not guilty

c) Type II error here is accepting that the defendent is not guilty even though he is guilty

d) Whenever type I increases type II error decreases and vice versa.

But as per ethics, an innocent person should not be punished at any cost, so care should be taken to avoid type I error which is more serious than avoiding type II error.