MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

Answer:The probabilities of Type I is 0.10.The probability of type II error is 0.3Step-by-step 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: [tex]Power=1-\beta[/tex]It is given that power is 0.7.Therefore,[tex]0.7=1-\beta[/tex][tex]\beta=1-0.7=0.3[/tex]Hence, the probability of type II error is 0.3