Question

(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 $\mu$=120 minutes: using $\alpha$=0.01 or $\alpha$=0.10? Explain.

Short answer

a. Type II error has been made

b. $\alpha =0.10$would give the test a higher power

Step-by-step solution

Introduction

Type-I error: Rejecting the genuine invalid hypothesis or it is otherwise called misleading positive.

Type-II error: Non-rejection of a misleading invalid hypothesis or it is otherwise called bogus negative.

Explanation Part (a)

Type I error - Concluding that the first-year students at the university concentrate under $2.5$hours of the night during the school week when they really review $2.5$hours of the night during the school week.

Type-II error- Concluding that the first-year students at the university review $2.5$hours of the night during the school week when they really concentrate under $2.5$hours out of every night during the school week.

From the above information, a Type II error has been made.

Explanation Part (b)

$\alpha =0.10$ would give the test a higher power as increasing the significance level maximises the power of the test.