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?