Question

One minus the power of the test is the probability that it will ________.

1) reject a true null hypothesis
2) reject a false null hypothesis
3) fail to reject a true null hypothesis
4) fail to reject a false null hypothesis

Answer 1

The phrase 'one minus the power of the test' refers to the probability of committing a Type II error, which is failing to reject a false null hypothesis.

Step-by-step explanation:

One minus the power of the test is the probability that it will fail to reject a false null hypothesis. This probability is known as the Type II error, represented by the Greek letter β (beta). The power of a test, defined as 1 − β, is the likelihood that the test correctly rejects a false null hypothesis. For example, if the power of a test is 0.981, the probability of a Type II error is 1 − 0.981 = 0.019, or 1.9%.

The four possible outcomes when performing a hypothesis test are:

• Correct decision not to reject H_o when H_o is true.
• Type I error: incorrectly rejecting H_o when H_o is true.
• Type II error: incorrectly failing to reject H_o when H_o is false.
• Correct decision to reject H_o when H_o is false.

Desirable outcomes in hypothesis testing are avoiding Type I and Type II errors, thus correctly accepting or rejecting the null hypothesis when it is indeed true or false, respectively.