7.9 Chapter 7 Formulas

Confidence Interval for One Proportion $\begin{aligned} &\hat{p} \pm z_{\frac{\alpha}{2}} \sqrt{\left(\frac{\hat{p q}}{n}\right)} \\ &\hat{p}=\frac{x}{n} \\ &\hat{q}=1-\hat{p} \end{aligned}$ TI-84: 1-PropZInt	Sample Size for Proportion $n=p^{} \cdot q^{}\left(\frac{z_{\alpha / 2}}{E}\right)^{2}$ Always round up to whole number. If p is not given use p* = 0.5. E = Margin of Error
Confidence Interval for One Mean Use z-interval when σ is given. Use t-interval when s is given. If n < 30, population needs to be normal.	Z-Confidence Interval $\bar{x} \pm z_{\frac{\alpha}{2}}\left(\frac{\sigma}{\sqrt{n}}\right)$ TI-84: ZInterval
Z-Critical Values Excel: z_{$\alpha$ /2} =NORM.INV(1–area/2,0,1) TI-84: z_{$\alpha$ /2} = invNorm(1–area/2,0,1)	t-Critical Values Excel: t_{$\alpha$ /2} =T.INV(1–area/2,df) TI-84: t_{$\alpha$ /2} = invT(1–area/2,df)
t-Confidence Interval $\bar{x} \pm t_{\alpha / 2}\left(\frac{s}{\sqrt{n}}\right)$ df = n – 1 TI-84: TInterval	Sample Size for Mean $n=\left(\frac{z_{\alpha / 2} \cdot \sigma}{E}\right)^{2}$ Always round up to whole number. E = Margin of Error

Adapted from Mostly Harmless Statistics by Rachel Webb (Portland State University, https://mostlyharmlessstat.wixsite.com/webpage), © Rachel Webb, licensed under CC BY-SA 4.0. Changes were made. License: CC-BY-SA-4.0.