Question:
Let \( X \) be a discrete random variable with probability mass function \( p \in \{p_0, p_1\} \), where
To test \( H_0 : p = p_0 \) against \( H_1 : p = p_1 \), the power of the most powerful test of size 0.05, based on \( X \), equals _________
Let \( X \) be a discrete random variable with probability mass function \( p \in \{p_0, p_1\} \), where
To test \( H_0 : p = p_0 \) against \( H_1 : p = p_1 \), the power of the most powerful test of size 0.05, based on \( X \), equals _________
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To calculate the power of a hypothesis test, compute the probability of rejecting the null hypothesis when the alternative hypothesis is true.
Updated On: Dec 29, 2025
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Correct Answer: 0.2
Solution and Explanation
To calculate the power of the most powerful test, we use the likelihood ratio test statistic and calculate the probability of rejecting \( H_0 \) when \( p = p_1 \). The power is the probability that the test correctly rejects the null hypothesis. Based on the given values, the power is approximately:
\[
\text{Power} = 0.20.
\]
Thus, the value is \( 0.20 \).
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