What is a Type I error?

Rejecting the null hypothesis when it is actually true.

What is a Type II error?

Not rejecting the null hypothesis when it is actually false.

What conditions define $\alpha$ and $\beta$?

$\alpha$ is calculated when $H_0$ is true; $\beta$ is calculated when $H_0$ is false.

How is the power of a test calculated?

Power is $1-\beta$, the probability of correctly rejecting a false null hypothesis.

How can increasing sample size affect test power?

A larger sample can increase power by providing more information about the population.

StatisticsLesson 2 of 5 in the course Hypothesis Testing with One Sample

Outcomes and Error Probabilities in Hypothesis Testing

5 flashcards · 5 quiz questions · 5 match pairs · 3 fill-in sentences · English

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Summary

A hypothesis test compares a decision about the null hypothesis with what is actually true. This lesson introduces the four possible outcomes and explains how the probabilities of errors and the power of a test are related.

A hypothesis test has two possible realities: the null hypothesis $H_0$ is either true or false. It also has two possible decisions: reject $H_0$ or do not reject $H_0$ . Combining these possibilities gives four outcomes.

All flashcards

What is a Type I error?: Rejecting the null hypothesis when it is actually true.
What is a Type II error?: Not rejecting the null hypothesis when it is actually false.
What conditions define $\alpha$ and $\beta$ ?: $\alpha$ is calculated when $H_0$ is true; $\beta$ is calculated when $H_0$ is false.
How is the power of a test calculated?: Power is $1-\beta$ , the probability of correctly rejecting a false null hypothesis.
How can increasing sample size affect test power?: A larger sample can increase power by providing more information about the population.

Quiz questions

What decisions can a hypothesis test make about the null hypothesis?Answer: Reject $H_0$ or do not reject $H_0$ .
What does a decision not to reject $H_0$ mean?Answer: The test did not provide sufficient evidence to reject $H_0$ .
Suppose $H_0$ states that climbing equipment is safe. The equipment is actually unsafe, but a test does not reject $H_0$ . What outcome occurred?Answer: A Type II error.
What determines whether a Type I or Type II error has more serious consequences?Answer: The consequences of acting on the mistaken conclusion in that setting.
How can increasing a test's sample size affect its power?Answer: It can increase power by providing more information about the population.

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

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