Solution Found!
Suppose Y is a random sample of size 1 from a population
Chapter 10, Problem 96E(choose chapter or problem)
Suppose is a random sample of size 1 from a population with density function
\(f\left(y \mid \theta=\left\{\begin{array}{l}
\theta y^{0-1}, 0 \leq y \leq 1, \\
0,
\end{array}\right.\right.
\)
where \(\theta>0\)
a Sketch the power function of the test with rejection region: \(Y>.5\).
b Based on the single observation , find a uniformly most powerful test of size for testing \(H_{0}: \theta=1\) versus \(H_{a}: \theta>1\).
Equation transcription:
Text transcription:
f\left(y \mid \theta=\left\{\begin{array}{l}
\theta y^{0-1}, 0 \leq y \leq 1, \\
0,
\end{array}\right.\right.
\theta>0
Y>.5
H_{0}: \theta=1
H_{a}: \theta>1
Questions & Answers
QUESTION:
Suppose is a random sample of size 1 from a population with density function
\(f\left(y \mid \theta=\left\{\begin{array}{l}
\theta y^{0-1}, 0 \leq y \leq 1, \\
0,
\end{array}\right.\right.
\)
where \(\theta>0\)
a Sketch the power function of the test with rejection region: \(Y>.5\).
b Based on the single observation , find a uniformly most powerful test of size for testing \(H_{0}: \theta=1\) versus \(H_{a}: \theta>1\).
Equation transcription:
Text transcription:
f\left(y \mid \theta=\left\{\begin{array}{l}
\theta y^{0-1}, 0 \leq y \leq 1, \\
0,
\end{array}\right.\right.
\theta>0
Y>.5
H_{0}: \theta=1
H_{a}: \theta>1
ANSWER:
Step 1 of 3
Given:
Suppose Y is a random sample of size 1 from a population with a density function
where > 0.