Hypothesis Tests: Tail Selection, P-Values, and Decision Methods

All flashcards

What is the significance level, $\alpha$?

A preset probability threshold for a hypothesis test, chosen before examining the sample results.

What does a p-value measure?

Assuming $H_0$ is true, it is the probability of a result at least as extreme as the observed result in the direction specified by $H_a$.

How does the alternative hypothesis determine a test's tail?

A less-than alternative is left-tailed, a greater-than alternative is right-tailed, and a not-equal-to alternative is two-tailed.

When does the usual p-value decision rule reject $H_0$?

When the p-value is less than or equal to the preset significance level, $\alpha$.

How do the p-value and critical-value methods differ?

The p-value method compares the p-value with $\alpha$; the critical-value method compares the test statistic with a cutoff.

Quiz questions

1. For a test with $\alpha=0.05$ and a p-value of $0.03$, what is the usual decision?Answer: Reject $H_0$ because the p-value is below $\alpha$.
2. Which formula gives the one-sample $z$ statistic for a population mean when $\sigma$ is known?Answer: $z=\frac{\bar{x}-\mu_0}{\sigma/\sqrt{n}}$
3. When using a calculator to find a hypothesis-test p-value, how should its alternative setting be chosen?Answer: Set it to match the direction specified by $H_a$.
4. For a left-tailed test, the critical value is $-1.645$ and the observed statistic is $-2.08$. What does the critical-value method conclude?Answer: Reject $H_0$, since the statistic is below the critical value.
5. In a hypothesis test about one population proportion, which symbol represents the population parameter?Answer: $p$