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% Document Info
\author{Natalie Moore (NatalieMoore)}
\pdfinfo{
  /Title (hypothesis-testing.pdf)
  /Creator (Cheatography)
  /Author (Natalie Moore (NatalieMoore))
  /Subject (Hypothesis Testing Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
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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{Hypothesis Testing Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Natalie Moore (NatalieMoore)} via \textcolor{DarkBackground}{\uline{cheatography.com/19119/cs/6012/}}}
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\noindent
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Natalie Moore (NatalieMoore) \\
  \uline{cheatography.com/nataliemoore} \\
        \uline{\seqsplit{www}.clipto.com/transcribe-audio-video-to-text-free?via=natalie}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 19th March, 2017.\\
   Updated 12th May, 2016.\\
   Page {\thepage} of \pageref{LastPage}.
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Statistical inference}}  \tn
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\mymulticolumn{2}{x{5.377cm}}{Draw conclusions from a set of data} \tn 
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\mymulticolumn{2}{x{5.377cm}}{Put a probability on whether a conclusion is correct 'beyond reasonable doubt'} \tn 
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\mymulticolumn{2}{x{5.377cm}}{The major question to answer is whether a difference between samples, or between a sample and a population, has occurred simply as a result of natural variation or because of a real difference between the two} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4977 cm} x{4.4793 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Two-tailed or one-tailed}}  \tn
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\mymulticolumn{2}{x{5.377cm}}{The alternative hypothesis may be classified as two-tailed or one-tailed} \tn 
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Two-tailed test}}} \tn 
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- & is a two-sided alternative \tn 
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- & we do the test with no preconceived notion that the true value of μ is either above or below the hypothesised value of μ 0 \tn 
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- & the alternative hypothesis is written:  H1: µ =/= µo \tn 
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\mymulticolumn{2}{x{5.377cm}}{{\bf{One-tailed test}}} \tn 
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- & one-sided alternative \tn 
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- & do the test with a strong conviction that, if H0 is not true, it is clear that m is either grater than µ0 or less than µ0 \tn 
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- & E.g. the alternative hypothesis is written as: H1: µ \textgreater{} µo \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\begin{tabularx}{5.377cm}{p{0.4977 cm} x{4.4793 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Decision-making process steps}}  \tn
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1. & Collecting the data \tn 
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2. & Summarising the data \tn 
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3. & Setting up a hypothesis (i.e. a claim or theory), which is to be tested \tn 
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4. & Calculating the probability of obtaining a sample such as the one we have if the hypothesis is true \tn 
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5. & Either accepting or rejecting the hypothesis \tn 
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\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Significance level}}  \tn
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\mymulticolumn{2}{x{5.377cm}}{After the appropriate hypotheses have been formulated, we must decide upon the significance level (or α -level) of the test} \tn 
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\mymulticolumn{2}{x{5.377cm}}{most common significance level used is 0.05, commonly written as α = 0.05} \tn 
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\mymulticolumn{2}{x{5.377cm}}{A 5\% significance level says in effect that an event has occurred that occurs less than 5\% of the time is considered unusual} \tn 
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\begin{tabularx}{5.377cm}{p{0.4977 cm} x{4.4793 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{One-sample z-test}}  \tn
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\mymulticolumn{2}{x{5.377cm}}{Deals with the case of a single sample being chosen from a population and the question of whether that particular sample might be consistent with the rest of the population} \tn 
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\mymulticolumn{2}{x{5.377cm}}{Construct a test statistic according to a particular formula} \tn 
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\mymulticolumn{2}{x{5.377cm}}{Information required in calculation} \tn 
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- & the size (n) of the sample \tn 
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- & the mean of the sample \tn 
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- & the standard deviation (s) of the sample \tn 
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\mymulticolumn{2}{x{5.377cm}}{Other information of interest might include:} \tn 
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- & Does the population have a normal distribution? \tn 
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- & Is the population's standard deviation known? \tn 
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- & Is the sample size (n) large? (25+) \tn 
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\mymulticolumn{2}{x{5.377cm}}{There are different cases for the one-sample z-test statistic} \tn 
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Case I }}} \tn 
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\mymulticolumn{2}{x{5.377cm}}{the population has a normal distribution and} \tn 
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\mymulticolumn{2}{x{5.377cm}}{the population standard deviation, s, is known} \tn 
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Case II }}} \tn 
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\mymulticolumn{2}{x{5.377cm}}{the population has any distribution} \tn 
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% Row 16
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\mymulticolumn{2}{x{5.377cm}}{the sample size, n, is large (i.e. at least 25), and} \tn 
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\mymulticolumn{2}{x{5.377cm}}{the value of population standard deviation is known} \tn 
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\mymulticolumn{2}{x{5.377cm}}{{\emph{In both these cases we can use a z-test statistic formula (a)}}} \tn 
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\begin{tabularx}{5.377cm}{p{0.4977 cm} x{4.4793 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{One-sample z-test (cont)}}  \tn
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Case III }}} \tn 
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\mymulticolumn{2}{x{5.377cm}}{the population has any distribution} \tn 
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\mymulticolumn{2}{x{5.377cm}}{the sample size, n, is large (i.e. at least 25), and} \tn 
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\mymulticolumn{2}{x{5.377cm}}{the value of population standard devation is unknown (however, since n is large, the value of population standard devation is approximated by the sample standard deviation, s)} \tn 
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% Row 23
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\mymulticolumn{2}{x{5.377cm}}{{\emph{In this case we can use a z-test statistic formula (b)}}} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Set up your Hypothesis}}  \tn
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Null Hypothesis}}} \tn 
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\mymulticolumn{2}{x{5.377cm}}{Part of formulation of an hypothesis} \tn 
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\mymulticolumn{2}{x{5.377cm}}{Statement that nothing unusual has occurred} \tn 
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\mymulticolumn{2}{x{5.377cm}}{The notation is Ho} \tn 
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Alternative hypothesis }}} \tn 
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\mymulticolumn{2}{x{5.377cm}}{States that something unusual has occurred} \tn 
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\mymulticolumn{2}{x{5.377cm}}{The notation is H1 or HA} \tn 
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\mymulticolumn{2}{x{5.377cm}}{{\bf{Together}} they may be written in the form:	Ho: (statement) v. H1(alternative statement)} \tn 
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\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Conclusion errors}}  \tn
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\mymulticolumn{2}{x{5.377cm}}{Two possible errors in making a conclusion about a null hypothesis} \tn 
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\mymulticolumn{2}{x{5.377cm}}{Type I errors occur when you reject H0 (i.e. conclude that it is false) when H0 is really true.} \tn 
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\mymulticolumn{2}{x{5.377cm}}{Type II errors occur when you accept H0 (i.e. conclude that it is true) when H0 is really false.} \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{z-test statistic formula (a)}}  \tn
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\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/nataliemoore_1446994473_2015-11-09 00_53_45-Photos.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{z-test statistic formula (b)}}  \tn
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\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/nataliemoore_1446994751_2015-11-09 00_57_27-Photos.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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% That's all folks
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