7.9: Chapter 7 Formulas

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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