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Chapter 9: Q 93. (page 609)

Error probabilities and power You read that a significance test at the α=0.01

significance level has probability 0.14of 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

Expert verified

Part (a) Power =0.86=86%

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

Step by step solution

01

Part (a) Step 1: Given information

P (Type II error) =0.14

α=0.01

02

Part (a) Step 2: Calculation

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

03

Part (b) Step 1: Explanation

The significance level αshows the probability of type I error.

P(TypeIerror)=α=0.01=1%

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