\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{clarekirk}
\pdfinfo{
  /Title (soci-271.pdf)
  /Creator (Cheatography)
  /Author (clarekirk)
  /Subject (SOCI 271 Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{82A397}
\definecolor{LightBackground}{HTML}{F7F9F8}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{SOCI 271 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{clarekirk} via \textcolor{DarkBackground}{\uline{cheatography.com/144494/cs/31026/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}clarekirk \\
  \uline{cheatography.com/clarekirk} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 10th March, 2022.\\
   Updated 13th March, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{1.34379 cm} x{3.63321 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Probability and Inferential Statistics}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Parameter }} & A number you derive from a population \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Statistic}} & A number you derive from a sample \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
{\bf{Census}} & A survey of the whole population \tn 
% Row Count 6 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Symbols}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/clarekirk_1646424894_GetImage.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.9908 cm} x{2.9862 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Probability \& Non-Probability Samples}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Probability Samples}} & Every case in the population has the same chance of being selected \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
{\bf{Non-Probability Samples}} & A specific group is being used as your sample. {\emph{Surveying students enrolled in a class}} \tn 
% Row Count 7 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Example}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{We want to know what \% of students work during the semester.  \newline % Row Count 2 (+ 2)
We draw a sample of 500 from a list of all students at the university  \newline % Row Count 4 (+ 2)
N = 20,000 (all students at university)  \newline % Row Count 5 (+ 1)
P = 500/20,000  \newline % Row Count 6 (+ 1)
Use a table of random numbers to selected 500 ID numbers with 6 digits  \newline % Row Count 8 (+ 2)
6 digits will be chosen 500 times until they match up with student numbers  \newline % Row Count 10 (+ 2)
After questioning each of these 500 students, we find that 368 (74\%) work during the semester.  \newline % Row Count 12 (+ 2)
{\bf{Population}} – 20,000  \newline % Row Count 13 (+ 1)
{\bf{Sample}} – 500  \newline % Row Count 14 (+ 1)
{\bf{Statistic}} – 74\%  \newline % Row Count 15 (+ 1)
{\bf{Parameter}} – Doesn't directly appear (it's implicit)  \newline % Row Count 17 (+ 2)
({\emph{\% of all students in the population who held a job}})% Row Count 19 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.84149 cm} x{3.13551 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Sampling Variation}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{Sample Statistics}} & Variables (e.g., sample mean, sample proportion) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
{\bf{Sampling Error}} & The sample will differ from the population purely by chance \tn 
% Row Count 5 (+ 3)
% Row 2
\SetRowColor{LightBackground}
Positive Sampling Error & Making the statistic exceed the population \tn 
% Row Count 7 (+ 2)
% Row 3
\SetRowColor{white}
Negative Sampling Error & Making the statistic less than the population parameter \tn 
% Row Count 10 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\emph{Sample statistic = population parameter + sampling error }} \newline  \newline {\bf{Sampling Distribution}}  \newline The theoretical, probabilistic distribution of a statistic for all possible samples of a given size (n).}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Construction of a Sampling Distribution}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/clarekirk_1646943789_Screen Shot 2022-03-10 at 12.22.54 PM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Statistic}} is used to estimate a parameter.  \newline Not all statistics will have the same value. \newline {\emph{What is the distribution of the values that we can get for the statistic?}} \newline  \newline {\bf{Standard Error}} = population standard error / square root of the population size}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Sampling Distribution}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/clarekirk_1646944466_Screen Shot 2022-03-10 at 12.34.08 PM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Practice Question}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{The average age for a population of doctors in a hospital is 51.6 years, What does this mean value represent?  \newline % Row Count 3 (+ 3)
{\bf{A parameter}} \newline % Row Count 4 (+ 1)
What does it mean for a sample to be representative  \newline % Row Count 6 (+ 2)
{\bf{The sample reproduces the important characteristics of the population}} \newline % Row Count 8 (+ 2)
Which set of symbols represents the standard deviation of the sampling distribution?  \newline % Row Count 10 (+ 2)
Which of these terms is synonymous with the standard error of the mean?  \newline % Row Count 12 (+ 2)
{\bf{The standard deviation of a sampling distribution}}% Row Count 14 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.64241 cm} x{3.33459 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Two Estimation Procedures}}  \tn
% Row 0
\SetRowColor{LightBackground}
Point Estimate & A sample statistic used to estimate a population parameter \tn 
% Row Count 3 (+ 3)
% Row 1
\SetRowColor{white}
Confidence Intervals & Consist of a range of values instead of a single point \tn 
% Row Count 6 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Example of point estimate: \newline 50\% of Canadians drive less because of gas. \newline  \newline Example of confidence: \newline Between 47\% and 53\% of Canadian drivers drive less due to high gas prices.  \newline  \newline {\bf{Confidence Intervals}} \newline - Point estimate is in the middle \newline - Lower and upper bound of C.I: 47\% and 53\% \newline - Margin of Error: radius or spread of the confidence interval (3\%)}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{0.9954 cm} x{3.9816 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Criteria for Choosing Estimators}}  \tn
% Row 0
\SetRowColor{LightBackground}
Bias & An estimator is unbiased if the mean of its sampling distribution is equal to the population value of interest \tn 
% Row Count 4 (+ 4)
% Row 1
\SetRowColor{white}
\seqsplit{Efficiency} & The extent to which the sampling distribution is clustered around its mean \tn 
% Row Count 7 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Bias}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/clarekirk_1646946013_GetImage (1).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{If n is large, we know that the sample mean/proportion is equal to the population parameter and: (image) \newline  \newline {\bf{Very good}} (68 out of 100 chances) that our sample outcome is within +/- 1 standard deviation of the true population parameter  \newline  \newline {\bf{Excellent}} (95 out of 100) that it is within +/- 3 standard deviations   \newline  \newline In less than 1\% of cases, a sample outcome will lie further away than +/- 3 standard deviations}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Efficiency}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/clarekirk_1646946093_GetImage (2).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Getting back to the matter of dispersion: standard error σx̄ (standard deviation of the sampling distribution) = σ/(√n)  \newline  \newline Standard error is an inverse function of n: as sample size increases, σx̄ will decrease  \newline  \newline The smaller the standard deviation of a sampling distribution, the greater the clustering and the higher the efficiency.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Constructing Confidence Intervals}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{1. Set the alpha, {\emph{a}} \newline % Row Count 1 (+ 1)
2. Find the Z score (or critical value) associated with alpha  \newline % Row Count 3 (+ 2)
3. Construct the confidence interval (we will substitute values into the appropriate formulas for confidence interval)% Row Count 6 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Constructing Confidence Intervals - Set the Alpha}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{1. Alpha = the probability that the interval will be wrong, I.e.,  it doesn't include the population parameter. \newline % Row Count 3 (+ 3)
The commonly used alpha level 0.05 corresponds to a 95\% confidence level. \newline % Row Count 5 (+ 2)
If an infinite number of intervals were constructed at the 0.50 alpha level (all other things being equal). 95\% of them would contain the population value; 5\% would not.% Row Count 9 (+ 4)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Constructing Confidence Intervals - Find Z Score}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/clarekirk_1646948925_GetImage (4).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{For an interval estimate based on +/-1.96 Z's:  \newline  \newline The probabilities are that 95\% of all such interval will include or overlap the population value  \newline  \newline We can be 85\% confident that the interval around our one sample outcome contains the population value}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Confidence Interval}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Point Estimate +/- Margin of Error  \newline % Row Count 1 (+ 1)
Point Estimate +/- (Critical Value * Standard Error)% Row Count 3 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{The margin of error depends on: \newline (1) the standard error for statistic AND  \newline (2) a "critical value/Z score" based on the confidence level}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Constructing Confidence Intervals for Proportions}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/clarekirk_1646949199_GetImage (5).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Point Estimate +/- (Critical Value/Score) x Standard Error)  \newline  \newline {\emph{for large samples (interval estimation for proportions based on small samples) (n\textless{}100) not covered)}}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Example}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/clarekirk_1646949714_GetImage (6).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{What proportion of students at your university missed at least one day of classes because of illness last semester?   \newline  \newline Out of a random sample of 200, 60 reported having missed classes: Ps = 60/200 = .30}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Confidence Intervals for Means}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/clarekirk_1646949817_GetImage (7).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{formula for large samples (n≥100)}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Example}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/clarekirk_1647022990_GetImage (9).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{You want to estimate the average IQ of a community using a random sample of 200 residents   \newline - with a sample mean IQ of 105   \newline - assuming a population standard deviation for IQ scores of 15   \newline Alpha set at .05 (i.e. we are willing to run a 5\% chance of being wrong).  \newline  \newline What is the corresponding Z score ?   \newline What is the formula?}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Conf}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/clarekirk_1647023135_Screen Shot 2022-03-11 at 10.24.37 AM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\emph{Three differences to Formula 6.1:}} \newline - σ is replaced by s   \newline - n is replaced by n–1 to correct for the fact that s is a biased estimator of σ  \newline  \newline To construct confidence intervals from sample means when s is unknown, we must use a different theoretical distribution, called the {\bf{Student's t distribution.}}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{T Distribution}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{The shape of the t distribution varies as a function of sample size. \newline % Row Count 2 (+ 2)
- Distribution is a family of curves, each curve is defined by its degrees of freedom – a value indicating the number of scores in a sample that are "free to vary" when calculating statistics.   \newline % Row Count 7 (+ 5)
- {\bf{Degrees of freedom (df = n–1).}} \newline % Row Count 8 (+ 1)
- As n increases, s becomes a more and more reliable estimator of the population standard deviation (σ)   \newline % Row Count 11 (+ 3)
{\emph{t distribution becomes more and more like the Z distribution.}}% Row Count 13 (+ 2)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{\{\{ac\}\} Smaller samples: t distribution is flatter and has heavier tails than Z distribution.   \newline   \newline The Z and t distribution are essentially identical when the sample size is greater than 100.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{T-Table Practice}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Find t score for alpha = 0.05 for n=30   \newline % Row Count 1 (+ 1)
Answers:   \newline % Row Count 2 (+ 1)
Degrees of freedom (df = n-1): 30 – 1 = 29   \newline % Row Count 3 (+ 1)
t score: ±2.045% Row Count 4 (+ 1)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}