Question

Let 𝑥1, 𝑥2, 𝑥3 and 𝑥4 be observed values of a random sample from an 𝑁(𝜃, 𝜎 2 ) distribution, where 𝜃∈ℝ and 𝜎>0 are unknown parameters. Suppose that 𝑥̅=$\frac{1}{4} ∑^4_{i=1} 𝑥_𝑖 = 3.6$ and $\frac{1}{3} ∑^4_{i=1} (𝑥_𝑖-\overline{x} )^2= 20.25$ . For testing the null hypothesis 𝐻0 ∶ 𝜃=0 against 𝐻1 ∶𝜃≠0, the 𝑝-value of the likelihood ratio test equals

• A. 0.712
• B. 0.208
• C. 0.104
• D. 0.052

Answer 1

Answer: (B)

0.208

Answer 2

The correct option is (B): 0.208