#set document(title: "7.9 Chapter 7 Formulas", author: "Rachel Webb")
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== 7.9#h(0.6em)Chapter 7 Formulas


    #figure(table(
  columns: 2, align: left, inset: 6pt,
  table.header([#strong[Confidence Interval for One Proportion]

            \\(\\begin{aligned} #linebreak() 
            &\\hat{p} \\pm z\_{\\frac{\\alpha}{2}} \\sqrt{\\left(\\frac{\\hat{p q}}{n}\\right)} \\\\ #linebreak() 
            &\\hat{p}=\\frac{x}{n} \\\\ #linebreak() 
            &\\hat{q}=1-\\hat{p} #linebreak() 
            \\end{aligned}\\)

            TI-84: 1-PropZInt], [#strong[Sample Size for Proportion]

            #math.equation(block: false, alt: "n equals p to the power * times q to the power * open parenthesis the fraction z sub α / 2 over E close parenthesis squared")[$n = p^(*) · q^(*) attach(( frac(z_(α / 2), E) ), t: 2)$]

            Always round up to whole number.

            If p is not given use p\* = 0.5.

            E = Margin of Error]),
  [#strong[Confidence Interval for One Mean]

            Use z-interval when σ is given.

            Use t-interval when s is given.

            If #emph[n] \< 30, population needs to be normal.], [#strong[Z-Confidence Interval]

            #math.equation(block: false, alt: "x bar ± z sub the fraction α over 2 open parenthesis the fraction σ over the square root of n close parenthesis")[$overline(x) ± z_(frac(α, 2)) ( frac(σ, sqrt(n)) )$]

            TI-84: ZInterval],
  [#strong[Z-Critical Values]

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            Excel: t#sub[#math.equation(block: false, alt: "α")[$α$]/2] =T.INV(1–area/2,#emph[df])

            TI-84: t#sub[#math.equation(block: false, alt: "α")[$α$]/2] = invT(1–area/2,#emph[df])],
  [#strong[t-Confidence Interval]

            #math.equation(block: false, alt: "x bar ± t sub α / 2 open parenthesis the fraction s over the square root of n close parenthesis")[$overline(x) ± t_(α / 2) ( frac(s, sqrt(n)) )$]

            #emph[df] = #emph[n] – 1

            TI-84: TInterval], [#strong[Sample Size for Mean]

            #math.equation(block: false, alt: "n equals open parenthesis the fraction z sub α / 2 times σ over E close parenthesis squared")[$n = attach(( frac(z_(α / 2) · σ, E) ), t: 2)$]

            Always round up to whole number.

            E = Margin of Error],
))