Question

Power and error A scientist calculates that a test at the α=0.05 significance level has probability 0.23 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 $=0.77=77\%$

Part (b) P (Type I error) $=0.05=5\%$

Step-by-step solution

Part (a) Step 1: Given information

$P(TypeIIerror)=0.23$

$\alpha =0.05$

Part (a) Step 2: Calculation

The probability of a type II error is multiplied by the power.

Consequently, the power is

$Power=1-P(TypeIIerror)=1-0.23=0.77=77\%$

Part (b) Step 1: Explanation

The type I error likelihood is represented by the significance level.

$P(TypeIerror)=\alpha =0.05=5\%$