54 Consider the analogy between making a decision about a hypothesis in a significance test and making a decision about the innocence or guilt of a defendant in a criminal trial. Iden- tify "Ho true." "Ho false" with "Defendant innocent. "Defendant guilty." and "Reject Ho." "Do not reject Ho" with "Convict defendant," "Acquit defendant."

a) Explain the difference between Type I and Type II cnors m this tial setting. Which type of error would you consider more serious and hope to set at a very small level? Why"

b) In this setting, explain why decreasing the chance of Type 1 error increases the chance of Type II error.