Hypothesis testing uses sample evidence to assess an assumption about a population. This lesson introduces the rare-event idea and explains how a p-value measures how surprising sample results would be if the null hypothesis were true.
A null hypothesis, written H0, is an assumption about a population that is treated as true for the purpose of evaluating sample evidence. It is not automatically a fact. We ask whether the observed data would be unusual if that assumption were true.
All flashcards
What is a p-value?
Assuming the null hypothesis is true, it is the probability of obtaining results at least as extreme as those observed.
What does the significance level represent?
The chosen threshold for a test; it is the probability of a Type I error.
What is a Type I error?
Rejecting the null hypothesis when it is actually true.
What does “do not reject the null hypothesis” mean?
The data do not provide sufficient evidence against the null hypothesis at the chosen significance level; this does not prove it true.
What should a contextual hypothesis-test conclusion include?
The test decision and what the evidence indicates about the population claim, without claiming certainty.
Quiz questions
When a test has p = 0.03 and the chosen significance level is α = 0.05, what decision follows?Answer: Reject the null hypothesis because the p-value is below the significance level.
What does the significance level α represent in a hypothesis test?Answer: The probability of rejecting the null hypothesis when it is true.
A test result leads a researcher not to reject the null hypothesis. What can the researcher conclude?Answer: The sample did not provide enough evidence against the null at the chosen level.
After rejecting a null hypothesis, what makes a conclusion appropriate for a real-world study?Answer: It states the decision and relates the evidence to the population claim without asserting certainty.
For a sample mean of 3 years, null mean of 2.5 years, population standard deviation of 1.5 years, and sample size 26, what is the one-sample z statistic?Answer: Approximately 1.70.
Based on Introductory Statistics 2e by Barbara Illowsky, Susan Dean (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.