the power of a significance test to reject the null hypothesis when a particular value of the alternative is…

the power of a significance test to reject the null hypothesis when a particular value of the alternative is true is 0.8. what is the probability that this test results in a type ii error?\n0.01\n0.05\n0.20\n0.80

the power of a significance test to reject the null hypothesis when a particular value of the alternative is true is 0.8. what is the probability that this test results in a type ii error?\n0.01\n0.05\n0.20\n0.80

Answer

Explanation:

Step1: Recall the relationship

The power of a test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. The probability of a Type - II error ($\beta$) is the probability of failing to reject the null hypothesis when the alternative hypothesis is true. The power of a test ($1-\beta$).

Step2: Calculate Type - II error probability

Given power = $0.8$. Since power = $1 - \beta$, we can solve for $\beta$. Rearranging the formula gives $\beta=1 -$ power. Substituting the given power value, we have $\beta = 1-0.8=0.2$.

Answer:

C. 0.20