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Chapter 9: Q 94. (page 609)

Power and error A scientist calculates that a test at the 伪=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鈥檚 the probability of making a Type I error?

Short Answer

Expert verified

Part (a) Power =0.77=77%

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

Step by step solution

01

Part (a) Step 1: Given information

P(TypeIIerror)=0.23

伪=0.05

02

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鈭�0.23=0.77=77%

03

Part (b) Step 1: Explanation

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

P(TypeIerror)=伪=0.05=5%

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Most popular questions from this chapter

Experiments on learning in animals sometimes measure how long it takes mice to find their way through a maze. The mean time is 18 seconds for one particular maze. A researcher thinks that a loud noise will cause the mice to complete the maze faster. She measures how long each of 10 mice takes with a loud noise as stimulus. The appropriate hypotheses for the significance test are

a. H0:渭=18;Ha:渭鈮�18

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c. H0:渭<18;Ha:渭=18

d. H0:渭=18;Ha:渭<18

e. H0:x炉=18;Ha:x炉<18

Flu vaccine A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults.

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