Refer to Exercise 8.8. Suppose we want to test H o : = 0 against the

Refer to Exercise 8.8. Suppose we want to test H_o: μ = 0 against the alternative H_a: μ > 0. Since the estimator of μ is µ̂ = y̅, the likelihood ratio test statistic is

Show that

Use the fact that Σⁿ_i=1 (y_i - y̅)² =  Σⁿ_i=1 y_i² - ny̅².

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.,

  

Transcribed Image Text:

L(Ho) L(0) %3D L(û) L(y)