Consider a radar system that uses radio waves to detect aircraft. The system receives a signal and, based on the received signal, it needs to decide whether an aircraft is present or not. Let X be the received signal. Suppose that we know X = W, if no aircraft is present. X = 1+ W, if an aircraft is present. where W- N(0, o? = }). Thus, we can write X = 0+ W, where 0 = 0 if there is no aircraft, and 0 = 1 if there is an aircraft. Suppose that we define Ho and H1 as follows: Họ (null hypothesis): No aircraft is present. H1 (alternative hypothesis): An aircraft is present. a. Write the null hypothesis, Ho, and the alternative hypothesis, H1, in terms of possible values of 0. b. Design a level 0.05 test (a = 0.05) to decide between Ho and H1. c. Find the probability of type Il error, B, for the above test. Note that this is the probability of missing a present aircraft.

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