Revision sheet

Interval estimates

Estimate ± ME, ME = critical value × SE; ME = half the width.

Watch out: width = 2 × ME.

Interval for p

$\hat{p} \pm z^*\sqrt{\hat{p}(1 - \hat{p})/n}$; check random and large counts.

Watch out: "confident", not "probability", for a computed interval.

Confidence level

$z^*$: 1.645, 1.96, 2.576. Higher confidence, wider interval.

Watch out: the level describes the method over many samples.

Sample size

$n \ge (z^*/ME)^2 p(1 - p)$, $p = 0.5$ if unknown; round up.

Watch out: halving ME needs 4 times the sample.

t interval for μ

$\bar{x} \pm t^* s/\sqrt{n}$, df $= n - 1$.

Watch out: t*, not z*, when σ is estimated.

Intervals for differences

Estimate difference ± critical value × √(sum of variances).

Watch out: does the interval contain 0?