Here, we look again at the radar problem (Example 8.23). More specifically, we observe the random variable X: X = + W, where W

Here, we look again at the radar problem (Example 8.23). More specifically, we observe the random variable X: X = θ + W, where W ∼ N(0,σ² = 1/9). We need to decide between

Let X = x. Design a level 0.05 test (α = 0.05) to decide between H₀ and H₁.

Example 8.23

Consider a rad ar 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

where W ∼ N(0,σ² = 1/9). Thus, we can write X = θ +W, where θ = 0 if there is no aircraft, and θ = 1 if there is an aircraft. Suppose that we define H₀ and H₁ as follows:

H₀ (null hypothesis): No aircraft is present.

H₁ (alternative hypothesis): An aircraft is present.

Ho: 0 = 0o = 0, H: 001.