What is a Type I error?

Rejecting a null hypothesis that is actually true. It is also described as rejecting a good null.

What is a Type II error?

Failing to reject a null hypothesis that is actually false.

What does “fail to reject $H_0$” mean?

The sample evidence was not strong enough to reject $H_0$ at the test’s chosen standard. It does not prove that $H_0$ is true.

What are the two correct test outcomes?

Fail to reject $H_0$ when it is true, and reject $H_0$ when it is false.

How can you identify an error in a scenario?

First identify whether $H_0$ is actually true or false, then compare that reality with the test decision. Rejecting a true null is Type I; failing to reject a false null is Type II.

Business statisticsLesson 1 of 2 in the course Hypothesis Testing with One Sample

Hypothesis-Test Outcomes, Error Probabilities, and Power

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

A hypothesis test compares a statistical decision with the actual, usually unknown, truth about the null hypothesis. This lesson introduces the four possible outcomes and the two kinds of errors.

Failing to reject is not the same as proving or accepting $H_0$ as true. A test makes a decision using sample evidence, while the actual state of the world may be either that $H_0$ is true or that it is false.

All flashcards

What is a Type I error?: Rejecting a null hypothesis that is actually true. It is also described as rejecting a good null.
What is a Type II error?: Failing to reject a null hypothesis that is actually false.
What does “fail to reject $H_0$ ” mean?: The sample evidence was not strong enough to reject $H_0$ at the test’s chosen standard. It does not prove that $H_0$ is true.
What are the two correct test outcomes?: Fail to reject $H_0$ when it is true, and reject $H_0$ when it is false.
How can you identify an error in a scenario?: First identify whether $H_0$ is actually true or false, then compare that reality with the test decision. Rejecting a true null is Type I; failing to reject a false null is Type II.

Quiz questions

What are the two possible decisions in a hypothesis test?Answer: Reject $H_0$ or fail to reject $H_0$ .
What are the two possible states of reality considered in a test of $H_0$ ?Answer: $H_0$ is true or $H_0$ is false.
A test fails to reject $H_0$ . What does that decision establish?Answer: There was insufficient evidence to reject $H_0$ ; it does not prove that $H_0$ is true.
What determines whether a Type I or Type II error has the more serious practical consequences?Answer: The context and consequences of the decision.
If $H_0$ states that a product has no effect, what must the data provide to support a claim that it does have an effect?Answer: Sufficient evidence against $H_0$ at the chosen significance standard.

Based on Introductory Business Statistics 2e by Alexander Holmes, Barbara Illowsky, Susan Dean (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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