Hypothesis Testing and P-Values Flashcards
What is hypothesis testing?
A statistical method used to determine if there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis.
What are the steps in hypothesis testing?
Formulate null and alternative hypotheses.
Set the significance level (𝛼).
Collect and analyze data.
Calculate test statistics.
Compare p-value with 𝛼 and make a decision.
What is the null hypothesis (𝐻0)?
The hypothesis that assumes no effect, difference, or relationship in the population.
What is the alternative hypothesis (𝐻1)?
The hypothesis that suggests there is an effect, difference, or relationship.
What is a p-value?
The probability of obtaining the observed results, or more extreme, if the null hypothesis is true.
How is the p-value interpreted?
If 𝑝≤𝛼, reject 𝐻0 (significant result).
If 𝑝>𝛼, fail to reject 𝐻0 (not significant).
What is the typical significance level used in hypothesis testing?
0.05 (5%), though 0.01 (1%) and 0.10 (10%) are also used depending on the context.
What is a Type I error?
Rejecting a true null hypothesis (false positive).
What is a Type II error?
Failing to reject a false null hypothesis (false negative).
How can Type I and Type II errors be minimized?
Decreasing the significance level reduces Type I error.
Increasing the sample size reduces Type II error.
What is the power of a hypothesis test?
The probability of correctly rejecting a false null hypothesis, calculated as
1−β.
What is a one-tailed test?
A test that examines if a parameter is greater than or less than a specified value in one direction.
What is a two-tailed test?
A test that examines if a parameter is significantly different from a specified value in either direction.
How does sample size affect hypothesis testing?
Larger samples provide more precise estimates and increase the power of the test.
What is the relationship between confidence intervals and hypothesis testing?
If the confidence interval does not contain the null hypothesis value, reject 𝐻0
