Question

Let 𝑋1, 𝑋2 be a random sample from a distribution having a probability density function
f(x) =\begin{cases} \frac{1}{θ}e^{\frac{y}{θ}} & \quad \text{if }x >0,\\\ 0, & \quad Otherwise \end{cases}$$𝜃
where 𝜃∈(0, ∞) is an unknown parameter. For testing the null hypothesis 𝐻0 : 𝜃=1 against 𝐻1∶ 𝜃≠1, consider a test that rejects 𝐻0 for small observed values of the statistic $𝑊 = \frac{𝑋_1+𝑋_2}{ 2}$ . If the observed values of 𝑋1 and 𝑋2 are 0.25 and 0.75, respectively, then the 𝑝-value equals___(round off to two decimal places)

Answer 1

The correct answer is: 0.25 to 0.27 (approx)