Refer to Exercises 8.8–8.10. Show that the rejection region for the likelihood ratio test is given by Z > z_α,where P(Z > z_α) = α. Under the assumption that H_O: μ = 0 is true, show that √n (y̅) is a standard normal random variable.

Data from Exercise 8.8

Suppose y₁, y₂, ..... y_n is a random sample from a normal distribution with unknown mean m and variance σ² = 1, i.e.,

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