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Chapter 9: Q. 78 (page 589)

Study more! The significance test in Exercise 76yields a P-value of 0.0622.

(a) Describe a Type I and a Type II error in this setting. Which type of error could you have made in Exercise 76? Why?

(b) Which of the following changes would give the test a higher power to detect μ=120minutes: using α=0.01or α=0.10? Explain.

Short Answer

Expert verified

a. Type II error since we failed to reject H0.

b. both α=0.01andα=0.1give the higher power.

Step by step solution

01

Given information

The significance test in Exercise 76yields a P-value of 0.0622.

02

Explanation (part a)

Type I error: experts conclude that student study hours has a higher mean yield when it actually doesn’t.

Type II error: experts conclude that there is a mean difference in yields when, in fact,

student study hours has a higher mean yield.

Type II error since we failed to reject H0.

03

Explanation (part b)

z(s) test statistics is:

z(s)=(x-μ₀)/s/√nz(s)=-30/8.22z(s)=-3.65

p-value for that z(s) p-value=0

Then for α=0.01or0.1;p-value<0.01or0.1

We are in the rejection region we need to reject H₀. Therefore, both localid="1650893185130" α=0.01andα=0.1give the higher power.

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Most popular questions from this chapter

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