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

(a) Explain what Type 1 and Type II errors are in the trial.

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

(c) Defendants are convicted ifthe jury findsthem to be guilty "beyond a reasonable doubt."

A jury interprets this to mean that if the defendantis innocent, the probability of being found guilty should be only 1 in a billion.

Describe any problems this strategy has.