A type of lie detector that measures brain waves was developed by a professor of neurobiology at Northwestern University (Associated Press, July 7, 1988). He said, “It would probably not falsely accuse any innocent people and it would probably pick up 70% to 90% of guilty people.” Suppose that the result of this lie detector test is allowed as evidence in a criminal trial as the sole basis of a decision between two rival hypotheses: accused is innocent versus accused is guilty. Although these are not “statistical hypotheses” (statements about a population characteristic), the possible decision errors are analogous to Type I and Type II errors.

In this situation, a Type I error is finding an innocent person guilty—rejecting the null hypothesis of innocence when it is in fact true. A Type II error is finding a guilty person innocent—not rejecting the null hypothesis of innocence when it is in fact false. If the developer of the lie detector is correct in his statements, what is the probability of a Type I error, α? What can you say about the probability of a Type II error, β?