08 Hypothesis Testing Free Online FlashCards

What is hypothesis testing?

A formal procedure that uses sample data to evaluate a claim about a population parameter.

What is the null hypothesis?

The default claim being tested, usually stating no difference, association, or effect; it includes equality, such as $H_0:\mu=\mu_0$.

What is the alternative hypothesis?

The hypothesis representing the effect or difference for which the investigation seeks evidence. It may be right-tailed, left-tailed, or two-tailed.

What does the significance level $\alpha$ represent?

The maximum probability of rejecting a true $H_0$; it controls the Type I error rate. Common choices are $0.10$, $0.05$, and $0.01$.

What does a test statistic measure?

A standardized measure of how far a sample result is from the value predicted by $H_0$, generally computed as $\frac{\text{observed estimate}-\text{null value}}{\text{standard error}}$.

What are common one-sample mean test statistics?

For a mean with known $\sigma$, use $z=\frac{\bar{x}-\mu_0}{\sigma/\sqrt{n}}$. For unknown $\sigma$, use $t=\frac{\bar{x}-\mu_0}{s/\sqrt{n}}$.

What is a p-value?

The probability, assuming $H_0$ is true, of obtaining a test statistic at least as extreme as observed in the direction specified by $H_a$.

How does the alternative determine the p-value tail?

For a right-tailed test, use the area to the right; for a left-tailed test, use the area to the left; for a two-tailed test, use both extreme directions.

What is the p-value decision rule?

Reject $H_0$ when $p\le\alpha$; fail to reject $H_0$ when $p>\alpha$.

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

Failing to reject $H_0$ means the data do not provide sufficient evidence against it; it does not prove or accept $H_0$.

What is a Type I error?

A Type I error is rejecting $H_0$ when it is true. Its probability is controlled by $\alpha$.

What is a Type II error?

A Type II error is failing to reject $H_0$ when it is false. Its probability is denoted by $\beta$.