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 hypotheses? b) What are...

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 hypotheses?
b) What are type I and type II errors in this case?
c) Which type of error is more costly?
d) Based on your answer to part(c), what value of α would you recommend for this test?
e) If the sensitivity of the metal detector is increased, how would the probabilities of type I and type II errors be affected?
f) If α is to be increased, should the sensitivity of the metal detector be increased or decreased?