Question

Error probabilities and power You read that a significance test at the $\alpha =0.01$

significance level has probability $0.14$of making a Type II error when a specific alternative is true.

a. What is the power of the test against this alternative?

b. What’s the probability of making a Type I error?

Short answer

Part (a) Power $=0.86=86\%$

Part (b) P (Type I error) $=0.01=1\%$

Step-by-step solution

Part (a) Step 1: Given information

P (Type II error) $=0.14$

$\alpha =0.01$

Part (a) Step 2: Calculation

The power is the complement of the probability of type II error, therefore the power is$Power=1-P(TypeIIerror)=1-0.14=0.86=86\%$

Part (b) Step 1: Explanation

The significance level $\alpha$shows the probability of type I error.

$P(TypeIerror)=\alpha =0.01=1\%$