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\author{allyrae97}
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  /Title (modern-business-statistics-interval-estimation.pdf)
  /Creator (Cheatography)
  /Author (allyrae97)
  /Subject (Modern Business Statistics Interval Estimation Cheat Sheet)
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Modern Business Statistics Interval Estimation Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{allyrae97} via \textcolor{DarkBackground}{\uline{cheatography.com/29652/cs/8745/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}allyrae97 \\
  \uline{cheatography.com/allyrae97} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 2nd August, 2016.\\
   Updated 2nd August, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Margin of Error and the Interval Estimate}}  \tn
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A point estimator cannot be expected to provide the  exact value of the population parameter. & An interval estimate can be computed by adding and  subtracting a margin of error to the point estimate. Point Estimate  +/-  Margin of Error \tn 
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The purpose of an interval estimate is to provide  information about how close the point estimate is to  the value of the parameter. & The general form of an interval estimate of a  population mean is: 𝑥 ̅ + Margin of Error \tn 
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Interval Estimate of a Pop. Mean: }}  \tn
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Interval Estimate: 𝑥 ̅± 𝑡(𝛼/2)  s/√𝑛 & 𝑥 ̅=the sample mean, 1-a=the confidence coefficient, t(a/2)=the t value providing an area of a/2 in the upper tail of a t distribution with n-1 degrees of freedom, s=the sample standard deviation, n=the sample size \tn 
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Interval Estimate of Mean: 𝑥 ̅± 𝑧(𝛼/2)  𝜎/√𝑛 & 𝑥 ̅ is the sample mean, 1-a is the confidence coefficient, z(a/2) is the z value providing an area of a/2 in the upper tail of the standard normal probability distribution, 𝜎 is the population standard deviation, n is the sample size \tn 
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Margin of Error: 𝐸=𝑧(𝛼/2)  𝜎/√𝑛 & Necessary Sample Size: n = 𝑧(𝛼/2) )\textasciicircum{}2 𝜎\textasciicircum{}2)/𝐸\textasciicircum{}2 \tn 
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The general form of an interval estimate of a population proportion is: 𝑝 ̅ + Margin of Error & Interval Estimate: \seqsplit{𝑝 ̅±𝑧(𝛼/2)} \seqsplit{√𝑝 ̅(1−𝑝 ̅)/𝑛)} \tn 
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Margin of Error: E = 𝑧(𝛼/2) \seqsplit{√𝑝 ̅(1−𝑝 ̅)/𝑛} & Necessary Sample Size: 𝑛=𝑧(𝛼/2)\textasciicircum{}2 𝑝∗ (1−𝑝∗ )/𝐸\textasciicircum{}2 \tn 
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% That's all folks
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