Hypothesis Testing — Basics
Big Idea:
Hypothesis testing is a formal statistical procedure that allows us to use sample data to make decisions about a population. It's like a courtroom trial — we start by assuming innocence (the null hypothesis) and look for evidence strong enough to reject that assumption.
Step 1: State the Hypotheses
Every hypothesis test begins with two competing statements:
- Null Hypothesis ($H_0$): The "default" claim — assumes no effect, no difference, or no change. This is what we assume to be true until evidence suggests otherwise.
- Alternative Hypothesis ($H_a$ or $H_1$): The claim we're trying to find evidence for. It contradicts $H_0$.
Example:
A company claims their light bulbs last 1000 hours on average.
$H_0: \mu = 1000$ (the claim is true)
$H_a: \mu \neq 1000$ (the claim is false)
A company claims their light bulbs last 1000 hours on average.
$H_0: \mu = 1000$ (the claim is true)
$H_a: \mu \neq 1000$ (the claim is false)
Types of Alternative Hypotheses
| Type | $H_a$ | Name |
|---|---|---|
| Two-tailed | $\mu \neq \mu_0$ | Not equal to |
| Left-tailed | $\mu < \mu_0$ | Less than |
| Right-tailed | $\mu > \mu_0$ | Greater than |
The direction of the alternative hypothesis determines where we look for evidence in the distribution — both tails, left tail only, or right tail only.