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?

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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?

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