Revision sheet

Hypotheses

H₀: parameter = value. Hₐ: <, >, or ≠.

Watch out: parameters, never statistics.

z test for p

$z = (\hat{p} - p_0)/\sqrt{p_0(1 - p_0)/n}$; P-value assumes H₀.

Watch out: use $p_0$ in the SE.

Conclusions and errors

• P ≤ α: reject H₀. Otherwise: fail to reject.
• Type I: reject true H₀. Type II: keep false H₀.
• Power rises with $n$.

Watch out: never "accept" or "prove" H₀.

t test for μ

$t = (\bar{x} - \mu_0)/(s/\sqrt{n})$, df $= n - 1$; two-sided: double the tail.

Watch out: failing to reject is not proving H₀.

Comparing two groups

• Two proportions: pooled $\hat{p}$ in the SE.
• Paired: test the differences.

Watch out: pool counts, not proportions.

Chi-square tests

$\chi^2 = \sum (O - E)^2/E$; GOF: $E = np$; two-way: $E =$ row × column / total.

Watch out: divide by $E$; use counts, not percentages.