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)
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)
\(f(x) =\begin{cases} \frac{1}{θ}e^{\frac{y}{θ}} & \quad \text{if }x >0,\\ 0, & \quad Otherwise \end{cases}\)\(𝜃\)
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)
Updated On: Oct 1, 2024
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Verified By Collegedunia
Correct Answer: 0.25
Solution and Explanation
The correct answer is: 0.25 to 0.27 (approx)
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