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Q50Section C (Section C)50 of 60

P-value for exponential scale test

Let X1,X2X_1, X_2 be a random sample from a distribution having a probability density function f(x;θ)={1θe−xθ,if x>0, 0,otherwise,f(x; \theta)=\begin{cases} \frac{1}{\theta} e^{-\frac{x}{\theta}}, & \text{if }x > 0, \ 0, & \text{otherwise,} \end{cases} where θ∈(0,∞)\theta\in(0, \infty) is an unknown parameter. For testing the null hypothesis H0:θ=1H_0: \theta=1 against H1:θ≠1H_1: \theta\neq 1, consider a test that rejects H0H_0 for small observed values of the statistic W=X1+X22W=\frac{X_1+X_2}{2}. If the observed values of X1X_1 and X2X_2 are 0.250.25 and 0.750.75, respectively, then the pp-value equals __________ (round off to two decimal places)

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