Question

You read that a statistical test at the α = 0.01 level has probability 0.38 of making a Type II error when a specific alternative is true. What is the power of the test against this alternative?

Answer 1

The power of the statistical test is 0.62, which is calculated as 1 - 0.38, the probability of a Type II error.

Step-by-step explanation:

If a statistical test at the α = 0.01 level has a probability of 0.38 of making a Type II error when a specific alternative is true, the power of the test against this alternative is calculated as 1 minus the probability of a Type II error. Therefore, the power of the test is 1 - 0.38, which equals 0.62.

The power of a statistical test is an important concept in hypothesis testing. It quantifies the likelihood that the test will correctly reject a false null hypothesis. A high power is desirable as it means the test is more likely to detect an effect or difference when it exists.

Mathematically, the power can be expressed as:

• Power = 1 - β, where β is the probability of a Type II error.