Question

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?

Answer 1

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:

$\text{Power = 1 - Type II error}$

Putting values, we get,

$0.85 = 1-P(\text{Type II error})\\P(\text{Type II error}) = 1-0.85 = 0.15$

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