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A test of significance was performed using α=5% . The P‑value was 4% and the power was 85% . What is the probability of a Type II error for this test?

Respuesta :

Answer:

0.15 is the probability of a Type II error for this test.

Step-by-step explanation:

We are given the following information in the question:

Alpha, α = 0.05 = 5%

P‑value = 4% = 0.04

Power of test = 85% = 0.85

We have to find the probability of a Type II error for this test.

  • The type II error is the error that occurs when we fails to reject a null hypothesis when it is false.
  • It is a false positive.
  • It is represented by β.

The relation between power of a  test and type II error is given as:

[tex]\text{Power = 1 - Type II error}[/tex]

Putting values, we get,

[tex]0.85 = 1-P(\text{Type II error})\\P(\text{Type II error}) = 1-0.85 = 0.15[/tex]

0.15 is the probability of a Type II error for this test.

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