t-Test for μ (Unknown σ)

Overview

The one-sample t-test tests hypotheses about the population mean when \(\sigma\) is unknown.

Test Statistic

\[ t = \frac{\bar{X} - \mu_0}{S / \sqrt{n}} \sim t_{n-1} \text{ under } H_0 \]

Assumptions

• Random sample from a Normal population (or large \(n\) by CLT)
• Independent observations

Robustness

The t-test is fairly robust to non-normality for moderate to large samples.