One-sample t-test: setup and assumptions.

easy

Answer

${\mu}\; = \;{\mu}_{0}$
$t\; = \;(X\; - \;{\mu}_{0})\; / \;(s\; / \; \sqrt n)$
$t_{n - 1}$
$Assumptions: (1) i.i.d. samples; (2) approximately normal (robust for n > 30 due to CLT).$
$Compare t to t-distribution quantiles or compute a p-value.$
$Use case: is the mean of a metric different from a target?$

Check yourself — multiple choice

No assumptions
$t\; = \;(X\; - \;{\mu}_{0}) / (s / \sqrt n)$ ~ $t_{n - 1}$ ; assumes i.i.d. + approx normal (robust at n > 30 via CLT)
Requires known σ
Only for two samples

One-sample t: $t = (X - {\mu}_{0}) / (s / \sqrt n)$ , df=n-1, robust past n≈30.

#hypothesis-testing#parametric-tests

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