8.6 Chapter 8 Formulas

Hypothesis Test for One Mean Use z-test when σ is given. Use t-test when s is given. If n < 30, population needs to be normal.	Type I Error- Reject H₀ when H₀ is true. Type II Error- Fail to reject H₀ when H₀ is false.
Z-Test: H₀: μ = μ₀ H₁: μ ≠ μ₀ $Z = \frac{\bar{x} - μ_{0}}{(\frac{σ}{\sqrt{n}})}$ TI-84: Z-Test	t-Test: H₀: μ = μ₀ H₁: μ ≠ μ₀ $t = \frac{\bar{x} - μ_{0}}{(\frac{s}{\sqrt{n}})}$ TI-84: T-Test
z-Critical Values Excel: Two-tail: $z sub α / 2$ = NORM.INV(1– $α$ /2,0,1) Right-tail: $z sub 1 minus α$ = NORM.INV(1– $α$ ,0,1) Left-tail: $z_{α}$ = NORM.INV( $α$ ,0,1) TI-84: Two-tail: $z sub α / 2$ = invNorm(1– $α$ /2,0,1) Right-tail: $z sub 1 minus α$ = invNorm(1– $α$ ,0,1) Left-tail: $z_{α}$ = invNorm( $α$ ,0,1)	t-Critical Values Excel: Two-tail: $t sub α / 2$ =T.INV(1– $α$ /2,df) Right-tail: $t sub 1 minus α$ = T.INV(1– $α$ ,df) Left-tail: $t_{α}$ = T.INV( $α$ ,df) TI-84: Two-tail: $t sub α / 2$ = invT(1– $α$ /2,df) Right-tail: $t sub 1 minus α$ = invT(1– $α$ ,df) Left-tail: $t_{α}$ = invT( $α$ ,df)
Hypothesis Test for One Proportion H₀: p = p₀ H₁: p ≠ p₀ $Z = \frac{\hat{p} - p_{0}}{\sqrt{(\frac{p_{0} q_{0}}{n})}}$ TI-84: 1-PropZTest	Rejection Rules: P-value method: reject H₀ when the p-value ≤ $α$ . Critical value method: reject H₀ when the test statistic is in the critical region (shaded tails).

Adapted from Mostly Harmless Statistics by Rachel Webb (Portland State University), hosted on LibreTexts (stats.libretexts.org) and licensed under CC BY-SA 4.0. Changes were made. License: CC-BY-SA-4.0.