Consider the use of metal detectors in airports to test people for concealed weapons. In essence, this is a form of hypothesis testing :
(a) What are the null and alternative hypothesis ?
(b) What are Type I and Type II errors in this case ?
(c) Which type of error is more costly ?
(d) If the sensitivity of the metal detector is increased, how would the probabilities of Type I and Type II errors be affected ?
(e) If Alpha is to be increased, should the sensitivity of the metal detector be increased or decreased?