A bag contains $N$ balls numbered $1,2,3,…,N$ to test the hypothesis $H_0 : N=10 $ vs $H_1:N=20.$ Draw $2$ balls from the bag without replacement, let $X$ denote the larger of the $2$ numbers in the drawn balls and reject $H_0$ if $X>9$. What is the power of this test?
My attempt.
When $H_1$ is true, $N=20$. And now we need to calculate the probability that $H_0$ is rejected which is $\frac{\binom{20}{2}-\binom{9}{2}}{\binom{20}{2}}$. Am I correct?
2026-03-31 09:25:46.1774949146
What is the power of this test?
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