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% Document Info
\author{GSarkar}
\pdfinfo{
  /Title (ap-stats-chapter-10.pdf)
  /Creator (Cheatography)
  /Author (GSarkar)
  /Subject (AP Stats Chapter 10 Cheat Sheet)
}

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\noindent
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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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\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{AP Stats Chapter 10 Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{GSarkar} via \textcolor{DarkBackground}{\uline{cheatography.com/76104/cs/18822/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}GSarkar \\
  \uline{cheatography.com/gsarkar} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 14th February, 2019.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{x{3.2 cm} x{4.8 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Two Proportion Confidence Interval}}  \tn
% Row 0
\SetRowColor{LightBackground}
Shape & When the large counts rule is met, the sampling distribution of p\textasciicircum{}1\textasciicircum{} - p\textasciicircum{}2\textasciicircum{} is approximately normal \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
Center & The mean of the sampling distribution is p\textasciicircum{}1\textasciicircum{} - p\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 8 (+ 3)
% Row 2
\SetRowColor{LightBackground}
Spread & The standard deviation of the sampling distribution of p\textasciicircum{}1\textasciicircum{} - p\textasciicircum{}2\textasciicircum{} is the square root of the sum of (p\textasciicircum{}1\textasciicircum{})(1-p\textasciicircum{}1\textasciicircum{}) divided by n\textasciicircum{}1\textasciicircum{} and (p\textasciicircum{}2\textasciicircum{})(1-p\textasciicircum{}2\textasciicircum{}) divided by n\textasciicircum{}2\textasciicircum{} as long as each sample is no more than 10\% of its population. \tn 
% Row Count 18 (+ 10)
% Row 3
\SetRowColor{white}
Conditions & Random (both samples must be random), 10\% (both samples less than 10\% of respective population), Large Counts (for both samples individually) \tn 
% Row Count 24 (+ 6)
% Row 4
\SetRowColor{LightBackground}
Calculator & 2-PropZInterval \tn 
% Row Count 25 (+ 1)
% Row 5
\SetRowColor{white}
Interpretation & We are \_\_\% confident that the interval from \_\_ to \_\_ captures the true difference of {[}p\textasciicircum{}1\textasciicircum{}{]} and {[}p\textasciicircum{}2\textasciicircum{}{]} \tn 
% Row Count 30 (+ 5)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.2 cm} x{4.8 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Two Proportion Confidence Interval (cont)}}  \tn
% Row 6
\SetRowColor{LightBackground}
Point Estimate Formula & p\textasciicircum{}1\textasciicircum{} - p\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 2 (+ 2)
% Row 7
\SetRowColor{white}
Critical Value Formula (Z*) & invNorm(\_\_\%/2 + 0.5) \tn 
% Row Count 4 (+ 2)
% Row 8
\SetRowColor{LightBackground}
Standard Deviation Formula & the square root of the sum of (p\textasciicircum{}1\textasciicircum{})(1-p\textasciicircum{}1\textasciicircum{}) divided by n\textasciicircum{}1\textasciicircum{} and (p\textasciicircum{}2\textasciicircum{})(1-p\textasciicircum{}2\textasciicircum{}) divided by n\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 8 (+ 4)
% Row 9
\SetRowColor{white}
Confidence Interval Formula & Point Estimate +/- Critical Value * Standard Deviation \tn 
% Row Count 11 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.92 cm} x{4.08 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Two Proportion Significance Test}}  \tn
% Row 0
\SetRowColor{LightBackground}
Null Hypothesis & p\textasciicircum{}1\textasciicircum{} - p\textasciicircum{}2\textasciicircum{} = Hypothesized Value \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Alternative Hypothesis & p\textasciicircum{}1\textasciicircum{} - p\textasciicircum{}2\textasciicircum{} \textasciitilde{}\textasciitilde{}=\textasciitilde{}\textasciitilde{} Hypothesized Value \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Conditions & Random (both), 10\% (both), Large Counts (both) \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
Pooled Sample Proportion & x\textasciicircum{}1\textasciicircum{} + x\textasciicircum{}2\textasciicircum{} / n\textasciicircum{}1\textasciicircum{} + n\textasciicircum{}2\textasciicircum{} (successes / size) \tn 
% Row Count 10 (+ 3)
% Row 4
\SetRowColor{LightBackground}
Statistic & p\textasciicircum{}1\textasciicircum{} - p\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 11 (+ 1)
% Row 5
\SetRowColor{white}
Parameter & Hypothesized Value (often 0) \tn 
% Row Count 13 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Standard Deviation & The square root of the sum of (p\textasciicircum{}c\textasciicircum{})(1-p\textasciicircum{}c\textasciicircum{}) divided by n\textasciicircum{}1\textasciicircum{} and (p\textasciicircum{}c\textasciicircum{})(1-p\textasciicircum{}c\textasciicircum{}) divided by n\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 18 (+ 5)
% Row 7
\SetRowColor{white}
Test Statistic Formula & Statistic - Parameter / Standard Deviation \tn 
% Row Count 21 (+ 3)
% Row 8
\SetRowColor{LightBackground}
Calculator & 2PropZTest \tn 
% Row Count 22 (+ 1)
% Row 9
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Areas of Error & Not a random sample = can't generalize results, cause and effect vs correlation \tn 
% Row Count 26 (+ 4)
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\SetRowColor{LightBackground}
IMPORTANT & If experimental units are randomly selected, check the 10\%, otherwise technically not necessary \tn 
% Row Count 31 (+ 5)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.92 cm} x{4.08 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Two Proportion Significance Test (cont)}}  \tn
% Row 11
\SetRowColor{LightBackground}
Ideal for Conclusions about Populations & Data from Two Independent Random Samples \tn 
% Row Count 3 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.84 cm} x{4.16 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Two Mean Confidence Interval}}  \tn
% Row 0
\SetRowColor{LightBackground}
Shape & When the population distributions are normal, the sampling distribution of x\textasciicircum{}1\textasciicircum{} - x\textasciicircum{}2\textasciicircum{} is approximately normal. Also normal, if both sample sizes are greater than 30 by CLT \tn 
% Row Count 9 (+ 9)
% Row 1
\SetRowColor{white}
Center & μ\textasciicircum{}1\textasciicircum{} - μ\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 10 (+ 1)
% Row 2
\SetRowColor{LightBackground}
Spread & If both samples are less than 10\% of respective populations, the formula for standard deviation is the square root of the sum of σ1\textasciicircum{}2\textasciicircum{} / n\textasciicircum{}1\textasciicircum{} and σ2\textasciicircum{}2\textasciicircum{} / n\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 18 (+ 8)
% Row 3
\SetRowColor{white}
Conditions & Random (both samples are independent and random or from two groups in a randomized experiment), 10\% (both), and Normal/Large (population distributions are normal or sample size greater than 30) \tn 
% Row Count 28 (+ 10)
% Row 4
\SetRowColor{LightBackground}
Calculator & 2SampTInt \tn 
% Row Count 29 (+ 1)
% Row 5
\SetRowColor{white}
Interpretation of a Confidence Level & If we take many samples of size \_ of \_ and of \_ of \_ and find the \_\_\% confidence interval for each sample, \_\_\% of the confidence intervals will capture the difference in the mean number of \_\_\_\_. \tn 
% Row Count 39 (+ 10)
\end{tabularx}
\par\addvspace{1.3em}

\vfill
\columnbreak
\begin{tabularx}{8.4cm}{x{3.84 cm} x{4.16 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Two Mean Confidence Interval (cont)}}  \tn
% Row 6
\SetRowColor{LightBackground}
Interpretation of Confidence Interval & We are \_\_\% confident that the interval from \_\_ to \_\_ captures the true difference in the \_\_ \tn 
% Row Count 5 (+ 5)
% Row 7
\SetRowColor{white}
State & We want to estimate μ\textasciicircum{}1\textasciicircum{} - μ\textasciicircum{}2\textasciicircum{} at the \_\_\% confidence level where μ\textasciicircum{}1\textasciicircum{} is \_\_ and μ\textasciicircum{}2\textasciicircum{} is \_\_ \tn 
% Row Count 10 (+ 5)
% Row 8
\SetRowColor{LightBackground}
Point Estimate Formula & x\textasciicircum{}1\textasciicircum{} - x\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 12 (+ 2)
% Row 9
\SetRowColor{white}
Critical Value Formula (t*) & invT(p/2 + 0.5, smaller n df) \tn 
% Row Count 14 (+ 2)
% Row 10
\SetRowColor{LightBackground}
Standard Deviation/Error Formula & The square root of the sum of σ1\textasciicircum{}2\textasciicircum{} / n\textasciicircum{}1\textasciicircum{} and σ2\textasciicircum{}2\textasciicircum{} / n\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 18 (+ 4)
% Row 11
\SetRowColor{white}
Confidence Interval Formula & Point Estimate +/- Critical Value * Standard Deviation \tn 
% Row Count 21 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{3.12 cm} x{4.88 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Two Mean Significance Test}}  \tn
% Row 0
\SetRowColor{LightBackground}
Null Hypothesis & μ\textasciicircum{}1\textasciicircum{} - μ\textasciicircum{}2\textasciicircum{} = Hypothesized Value \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Alternative Hypothesis & μ\textasciicircum{}1\textasciicircum{} - μ\textasciicircum{}2\textasciicircum{} \textasciitilde{}\textasciitilde{}=\textasciitilde{}\textasciitilde{} Hypothesized Value \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Conditions & Random (both), 10\% (both), Normal/Large (both)(no strong skew, outliers, or greater than 30) \tn 
% Row Count 8 (+ 4)
% Row 3
\SetRowColor{white}
Statistic & x\textasciicircum{}1\textasciicircum{} - x\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 9 (+ 1)
% Row 4
\SetRowColor{LightBackground}
Parameter & μ\textasciicircum{}1\textasciicircum{} - μ\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 10 (+ 1)
% Row 5
\SetRowColor{white}
Standard Deviation & The square root of the sum of s1\textasciicircum{}2\textasciicircum{} / n\textasciicircum{}1\textasciicircum{} and s2\textasciicircum{}2\textasciicircum{} / n\textasciicircum{}2\textasciicircum{} \tn 
% Row Count 13 (+ 3)
% Row 6
\SetRowColor{LightBackground}
Test Statistic Formula (T) & Statistic - Parameter / Standard Deviation \tn 
% Row Count 15 (+ 2)
% Row 7
\SetRowColor{white}
Calculator & 2SampTTest \tn 
% Row Count 16 (+ 1)
% Row 8
\SetRowColor{LightBackground}
Interpretation of p-value & Assuming the null hypothesis is true, there is a \_\_ probability of getting a difference in \_\_\_ just by the chance involved in random assignment/variability \tn 
% Row Count 23 (+ 7)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Paired Data vs Two Samples}}  \tn
% Row 0
\SetRowColor{LightBackground}
Paired Data & Two Samples \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Subjects were paired and the split at random into the two treatment groups or each subject received both treatments in a random order & Experimental groups were formed using randomized design or two independent random samples were taken from the population \tn 
% Row Count 8 (+ 7)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


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

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