Question

# We have specified the "tailedness" of a hypothesis test for a population mean with null hypothesis $H_{0}: \mu=\mu_{0}$. For each exercise. a. draw the ideal power curve. b. explain what your curve in part (a) portrays. two-tailed

Solution

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(a) The power is the probability of rejecting the null hypothesis when the alternative hypothesis is true.

Since the test is right-tailed, the alternative hypothesis is of the form $H_a:\mu\neq\mu_0$.

The ideal power is then 1 for any value of $\mu$ different from $\mu_0$, because we would then reject the null hypothesis $H_0:\mu=\mu_0$ whenever the alternative hypothesis $H_a:\mu\neq\mu_0$ is true.

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