Question

1. You read that a statistical test at the α = 0.01 level has probability 0.18 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative?
2. You read that a statistical test at the α = 0.01 level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative?

Answer 1

Question #8259 1. You read that a statistical test at the $\alpha=0.01$ level has probability 0.18 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative? 2. You read that a statistical test at the $\alpha=0.01$ level has probability 0.14 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative?

Solution. The power of the test equals $1-\mathsf{P}(\text{Type II error})=1-0.18=0.82$ in the first case and $1-0.14=0.86$ in the second.

Answer. 1) 0.82, 2) 0.86.