Let 𝑥 1 , 𝑥 2 , 𝑥 3 and 𝑥 4 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 𝐻 0 ∶ 𝜃=0 against 𝐻 1 ∶𝜃≠0, the 𝑝-value of the likelihood ratio test equals

The correct option is (B): 0.208

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= 1 4 ∑ 𝑥𝑖 = 3.6 4 𝑖=1 and 1 3 ∑ (𝑥𝑖 − 𝑥̅) 4 2 𝑖=1 = 20.25 . For testing the null hypothesis 𝐻0 ∶ 𝜃 = 0 against 𝐻1 ∶ 𝜃 ≠ 0, the 𝑝-value of the likelihood ratio test equals