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Chapter 10: Problem 22

One type of error in a hypothesis test is failing to reject a false null hypothesis. What is the other type of error that might occur when a hypothesis test is carried out?

Short Answer

Expert verified
The other type of error that might occur when a hypothesis test is carried out, apart from failing to reject a false null hypothesis, is rejecting a true null hypothesis, also known as a Type I error.

Step by step solution

01

Understand the Question

We are tasked to identify the other type of error in a hypothesis test apart from failing to reject a false null hypothesis. From statistical theory, we know there are two types of errors in hypothesis testing: Type I and Type II.
02

Define Error Types

A Type I error occurs when we reject a true null hypothesis (a 'false positive'), while a Type II error occurs when we fail to reject a false null hypothesis (a 'false negative').
03

Identify the Requested Error Type

The exercise already mentioned the scenario when we fail to reject a false null hypothesis, which is Type II error. Hence, the other error type not mentioned is Type I error, when we reject a true null hypothesis.

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Most popular questions from this chapter

Give an example of a situation where you would not want to select a very small significance level.

An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is expensive, so it will be done only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers. Let \(p\) denote the actual proportion of defective installations for the robots. It is known that the proportion of defective installations for human assemblers is 0.02 . a. Which of the following pairs of hypotheses should the manufacturer test? $$H_{0}: p=0.02 \text { versus } H_{a}: p<0.02$$ or $$H_{0}: p=0.02 \text { versus } H_{a}: p>0.02$$ Explain your choice. b. In the context of this exercise, describe Type I and Type II errors. c. Would you prefer a test with \(\alpha=0.01\) or \(\alpha=0.10 ?\) Explain your reasoning.

Which of the following are legitimate hypotheses? a. \(p=0.65\) b. \(\hat{p}=0.90\) c. \(\hat{p}=0.10\) d. \(p=0.45\) e. \(p>4.30\)

A television manufacturer states that at least \(90 \%\) of its TV sets will not need service during the first 3 years of operation. A consumer group wants to investigate this statement. A random sample of \(n=100\) purchasers is selected and each person is asked if the set purchased needed repair during the first 3 years. Let \(p\) denote the proportion of all sets made by this manufacturer that will not need service in the first 3 years. The consumer group does not want to claim false advertising unless there is strong evidence that \(p<0.9\). The appropriate hypotheses are then \(H_{0}: p=0.9\) versus \(H_{a}: p<0.9\). a. In the context of this problem, describe Type I and Type II errors, and discuss the possible consequences of each. b. Would you recommend a test procedure that uses \(\alpha=\) 0.01 or one that uses \(\alpha=0.10 ?\) Explain.

Explain why a \(P\) -value of 0.0002 would be interpreted as strong evidence against the null hypothesis.
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