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 _________ 

Hint:

To calculate the power of a hypothesis test, compute the probability of rejecting the null hypothesis when the alternative hypothesis is true.

Answer 1

Correct Answer: 0.2

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 \( 0.20 \).