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\author{allyrae97}
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  /Title (chapter-7-sampling-and-sampling-distributions.pdf)
  /Creator (Cheatography)
  /Author (allyrae97)
  /Subject (Chapter 7: Sampling and Sampling Distributions Cheat Sheet)
}

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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Chapter 7: Sampling and Sampling Distributions Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{allyrae97} via \textcolor{DarkBackground}{\uline{cheatography.com/29652/cs/8742/}}}
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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 1st 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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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Definitions}}  \tn
% Row 0
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Element: The entity on which data are collected & Population: A collection of all the elements of interest \tn 
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\mymulticolumn{2}{x{8.4cm}}{} \tn 
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Sample: A subset of the population & Sampled population: The population from which the sample is collected \tn 
% Row Count 7 (+ 4)
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\mymulticolumn{2}{x{8.4cm}}{Frame: a list of elements that the sample will be collected from} \tn 
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Sampling from an Infinite Population}}  \tn
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Populations generated by an ongoing process are referred to as Infinite Populations: parts being manufactured, transactions occurring at a bank, calls at a technical help desk, customers entering a store & Each element selected must come from the population of interest, Each element is selected independently. \tn 
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Sampling Distribution of}}  \tn
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Expected value of 𝑥 ̅: E(𝑥 ̅) = u & Standard Deviation of 𝑥 ̅ : \tn 
% Row Count 3 (+ 3)
% Row 1
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Finite Population: 𝜎𝑥 ̅ \seqsplit{=√𝑁−𝑛/(𝑁−1))} (𝜎/√𝑛) & Infinite Population: 𝜎𝑥 ̅ =𝜎/√𝑛 \tn 
% Row Count 7 (+ 4)
% Row 2
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Z-value at the upper endpoint of interval=largest \seqsplit{value-u/𝜎𝑥 ̅} & Area under the curve to the left of the upper endpoint=largest \seqsplit{value-u/𝜎𝑥 ̅}  on the z table \tn 
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% Row 3
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Z-value at the lower endpoint of the interval=smallest \seqsplit{value-u/𝜎𝑥 ̅} & Area under the curve to the left of the lower endpoint=smallest \seqsplit{value-u/𝜎𝑥 ̅}  on the z table \tn 
% Row Count 17 (+ 5)
% Row 4
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Probability=area under curve to left of upper endpoint-area under curve to left of lower endpoint & When selecting a different sample number, expected value remains the same. When the sample size is increased the standard error is decreased. \tn 
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Sampling from a Finite Population}}  \tn
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Finite Populations are often defined by lists: Organization Member Roster, Credit Card Account Numbers, Inventory Product Numbers & A simple random sample of size n from a finite population of size N: a sample selected such that each possible sample of size n has the same probability of being selected \tn 
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Point Estimation}}  \tn
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Point Estimation is a form of statistical inference. & We use the data from the sample to compute a value of a sample statistic that serves as an estimate of a population parameter. \tn 
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𝑥 ̅ is the point estimator of the population mean & s is the point estimator of the population standard deviation \tn 
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𝑝 ̅ is the point estimator of the population proportion & \seqsplit{𝑥 ̅=(∑𝑥𝑖} )/n \tn 
% Row Count 15 (+ 4)
% Row 3
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𝑠=√∑(𝑥𝑖-𝑥 ̅)\textasciicircum{}2/n-1 & 𝑝 ̅=x/n \tn 
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Expected value of \seqsplit{𝑝 ̅=E(𝑝 ̅)=𝑝} & Standard Deviation of 𝑝 ̅; \tn 
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% Row 1
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Finite Population: 𝜎𝑝 ̅ \seqsplit{=√𝑁−𝑛/(𝑁−1))(} \seqsplit{√𝑝(1−𝑝/𝑛)} & Infinite Population: 𝜎𝑝 ̅ \seqsplit{=√𝑝(1−𝑝/𝑛} \tn 
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Z-value at the upper endpoint of the interval=largest value-p/ 𝜎𝑝 ̅ & Area under the curve to the left of the upper endpoint equals z value of largest value-p/ 𝜎𝑝 ̅ \tn 
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Z-value at the lower endpoint of the interval=smallest value-p/ 𝜎𝑝 ̅ & Area under the curve to the left of the lower endpoint=z=value of mallest value-p/ 𝜎𝑝 ̅ \tn 
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% That's all folks
\end{multicols*}

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