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Chapter 9: Problem 8

Consider \(H_{0}: \mu=55\) versus \(H_{1}: \mu \neq 55\). a. What type of error would you make if the null hypothesis is actually false and you fail to reject it? b. What type of error would you make if the null hypothesis is actually true and you reject it?

Short Answer

Expert verified
a. If the null hypothesis \(H_{0}: \mu = 55\) is false and isn't rejected, a Type II error would be made. b. If the null hypothesis \(H_{0}: \mu = 55\) is true but is rejected, a Type I error would be made.

Step by step solution

01

Understanding Type Errors in Hypothesis Testing

In hypothesis testing, two types of errors can occur and they are often given the labels Type I and Type II. A Type I error occurs when the null hypothesis (H0) is true, but is rejected. A Type II error occurs when the null hypothesis is false, but is failed to be rejected.
02

Identifying Type I Error

Type I error would occur in case the null hypothesis \(H_{0}: \mu=55\) is actually true but it has been rejected. This could lead to taking an action that is not needed since the null hypothesis was actually true.
03

Identifying Type II Error

Type II error would occur in case the null hypothesis \(H_{0}: \mu=55\) is actually false but failed to be rejected. This may result in not taking a necessary action since in reality the null hypothesis was false.

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Most popular questions from this chapter

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