Critical values

Definition

Critical values are specific points in a probability distribution that mark the boundaries for rejecting or failing to reject a null hypothesis. They correspond to the chosen significance level $(\alpha)$ and are used to determine whether a test statistic falls within the rejection region.

5 Must Know Facts For Your Next Test

1. Critical values depend on the significance level $(\alpha)$, commonly set at 0.05, 0.01, or 0.10.
2. They differ based on the type of test being conducted (e.g., one-tailed vs two-tailed tests).
3. In a standard normal distribution, critical values can be found using $z$-scores.
4. For t-distributions, critical values vary depending on degrees of freedom.
5. Using critical values helps decide whether to reject the null hypothesis by comparing them against calculated test statistics.

Review Questions

• How do you determine the critical value for a two-tailed test with a significance level of $\alpha = 0.05$?
• Explain how critical values are used in hypothesis testing.
• What is the relationship between critical value and significance level?

Related terms

Significance Level: The probability of rejecting the null hypothesis when it is actually true; denoted by $\alpha$.

$z$-Score: A measure of how many standard deviations an element is from the mean.

p-Value: The probability that observed data would occur if the null hypothesis were true.