One Sample, Three Null Hypotheses

A theater checks the timing of a lighting controller. One sample is tested against three different null hypotheses.

One sample, three tests

Each curve is the distribution of x̄ assuming that test’s H0 is true (σ/√n = 1 ms).

Observed x̄, the same sample in every test As extreme as or more extreme than x̄: area = P μ0, the mean if H0 is true

Not rejecting H0 does not mean that H0 is true.

2.0 ms