Consider the analogy between making a decision in a test and making a decision about the innocence or guilt of a defendant in a criminal trial.

(a) Explain what Type I and Type II errors are in the trial.

(b) Explain intuitively why decreasing P(Type I error) increases P(Type II error).

(c) Defendants are convicted if the jury finds them to be guilty “beyond a reasonable doubt.”A jury interprets this to mean that if the defendant is innocent, the probability of being found guilty should be only 1 in a billion. Describe any disadvantages this strategy has.