A test has power $0.85$ when $\mu _ { 1 } = 21$.
True or false: the probability of making a correct decision when $\mu _ { 1 } = 21$ is $0.15$.

Question

A test has power $0.85$ when $\mu _ { 1 } = 21$. 
True or false: the probability of making a correct decision when $\mu _ { 1 } = 21$ is $0.15$.

Quizplus · Accepted Answer

Power is the probability of correctly rejecting a false null hypothesis. Therefore, if the null hypothesis is not true (meaning the true mean is different from the null), the power will be higher. Since the power is 0.85 when the true mean is 21, the probability of making a correct decision (which means rejecting the null hypothesis) is higher than 0.15. In fact, the probability of making a correct decision is 0.85.

A Test Has Power 0.850.850.85 When μ1=21\mu _ { 1 } = 21μ1​=21

A Test Has Power $0.85$ When $\mu _ { 1 } = 21$