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Cheat Sheet: One-Sample t-Test

This is a parametric test for a single random variable $X$. It is used to test whether the expectation is equal to a hypothesized value, $\mu_0$. For example, you can use a one-sample t-test to compare a sample of sleep times against the benchmark of 8 hours per night.

Assumptions:

  1. Metric scale.
    • In particular, the t-test is not valid for variables which only have an ordinal structure.
  2. IID data.
  3. No major deviations from normality, considering the sample size.
    • In particular, the t-test is invalid for highly skewed distributions when sample size is less than 30. It may also be invalid for very highly skewed distributions at higher sample sizes.

Null Hypothesis

The expectation of $X$ is equal to a reference mean $\mu_0$.