The Null Hypothesis
The null hypothesis (H₀) is the skeptic’s default: nothing special is happening — no difference, no effect, the coin is fair, the bags weigh what the label says. Statistical testing never proves your idea directly; it asks whether the data is surprising enough to reject the boring explanation.
The setup
| Example (bag weights) | |
|---|---|
| H₀ (null) | μ = 500g — the label is right |
| H₁ (alternative) | μ ≠ 500g — something’s off (two-tailed) |
Then a z-test (or t-test) measures how far your sample sits from H₀’s claim, and the p-value from the z table says how surprising that distance would be if H₀ were true. Small p → reject H₀. Large p → fail to reject — which is not the same as proving H₀ true; absence of evidence isn’t evidence of absence.
The two ways to be wrong
Type I error: rejecting a true null — a false alarm; its probability is the significance level α you chose (usually 5%). Type II error: failing to reject a false null — a miss, more likely with small samples and small effects. The α = 0.05 convention is simply a chosen trade-off between the two, not a law of nature — which is why serious work reports the p-value and a confidence interval rather than just "significant or not."