Question

Let 𝑋 be a random variable having a probability density function
$f(x; θ) =\begin{cases} (3-θ){x^2-θ} & \quad \text{if }0<x<1,\\\ 0, & \quad Otherwise \end{cases}$
where 𝜃 ∈ {0, 1}. For testing the null hypothesis 𝐻0 : 𝜃=0 against 𝐻1 : 𝜃=1, the power of the most powerful test, at the level of significance 𝛼=0.125, equals

• A. 0.15
• B. 0.25
• C. 0.35
• D. 0.45

Answer 1

Answer: (B)

0.25

Answer 2

The correct option is (B): 0.25