Question

You read that a study is planned for which a test of hypothesis will be done at significance level α = 0.10. Statisticians have calculated that for a certain effect size, the power is 0.7. What are the probabilities of Type I and Type II errors for this test?

Answer 1

The probabilities of Type I is 0.10.

The probability of type II error is 0.3

Explanation:

Consider the provided information.

Type I error: If we reject the null hypothesis when null hypothesis is true then it is called type I error.

The type I error is denoted by α.

Type II error: If we fail to reject the null hypothesis when null hypothesis is false then it is called type II error.

The type II error is denoted by β.

It is given that significance level α = 0.10.

Thus, the probabilities of Type I is 0.10.

The power of the test is:
`Power=1-\beta`

It is given that power is 0.7.

Therefore,

`0.7=1-\beta`

`\beta=1-0.7=0.3`

Hence, the probability of type II error is 0.3