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tabellen.tex
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\subsubsection{Quantilen der Normalverteilung}
\begin{itemize}
\item Verteilungsfunktion der standardisierten Normalverteilung: $F(x) = p$
\end{itemize}
\begin{figure}[!h]
\begin{center}
\scriptsize
\begin{tabular}{|l|r||l|r|}
\hline
$p$&$x$ & $p$ & $x$ \\
\hline
0.75&0.6745 & 0.25 & -0.6745 \\
0.8&0.8416 & 0.2 & -0.8416 \\
0.9&1.2816 & 0.1 & -1.2816 \\
0.95&1.6449 & 0.05 & -1.6449 \\
0.975&1.9600 & 0.025 & -1.9510 \\
0.99&2.3263 & 0.01 & -2.3263 \\
0.995&2.5758 & 0.005 & -2.5758 \\
0.999&3.0902 & 0.001 & -3.0902 \\
0.9995&3.2905 & 0.0005 & -3.2905 \\
\hline
\end{tabular}
\end{center}
\end{figure}
\begin{itemize}
\item Muss Standardisiert sein: Mit $E(X) = 0$ und $\operatorname{var} = 1$
\item $1-p = -x$
\item In \texttt{R}: \texttt{qnorm(p)}
\item Mit \texttt{TI-Nspire}: \texttt{invNorm($p,E(X),\operatorname{var}$)} bzw. \texttt{normCdf($-\infty,x,E(X),\operatorname{var}$)}
\end{itemize}
\pagebreak
\subsubsection{Verteilungsfunktion der Normalverteilung}
\begin{figure}[!h]
\begin{center}
\scriptsize
\begin{tabular}{|r|rrrrrrrrrr|}
\hline
$x$&+0.00&+0.01&+0.02&+0.03&+0.04&+0.05&+0.06&+0.07&+0.08&+0.09\\
\hline
0.0&0.5000&0.5040&0.5080&0.5120&0.5160&0.5199&0.5239&0.5279&0.5319&0.5359\\
0.1&0.5398&0.5438&0.5478&0.5517&0.5557&0.5596&0.5636&0.5675&0.5714&0.5753\\
0.2&0.5793&0.5832&0.5871&0.5910&0.5948&0.5987&0.6026&0.6064&0.6103&0.6141\\
0.3&0.6179&0.6217&0.6255&0.6293&0.6331&0.6368&0.6406&0.6443&0.6480&0.6517\\
0.4&0.6554&0.6591&0.6628&0.6664&0.6700&0.6736&0.6772&0.6808&0.6844&0.6879\\
0.5&0.6915&0.6950&0.6985&0.7019&0.7054&0.7088&0.7123&0.7157&0.7190&0.7224\\
0.6&0.7257&0.7291&0.7324&0.7357&0.7389&0.7422&0.7454&0.7486&0.7517&0.7549\\
0.7&0.7580&0.7611&0.7642&0.7673&0.7704&0.7734&0.7764&0.7794&0.7823&0.7852\\
0.8&0.7881&0.7910&0.7939&0.7967&0.7995&0.8023&0.8051&0.8078&0.8106&0.8133\\
0.9&0.8159&0.8186&0.8212&0.8238&0.8264&0.8289&0.8315&0.8340&0.8365&0.8389\\
1.0&0.8413&0.8438&0.8461&0.8485&0.8508&0.8531&0.8554&0.8577&0.8599&0.8621\\
1.1&0.8643&0.8665&0.8686&0.8708&0.8729&0.8749&0.8770&0.8790&0.8810&0.8830\\
1.2&0.8849&0.8869&0.8888&0.8907&0.8925&0.8944&0.8962&0.8980&0.8997&0.9015\\
1.3&0.9032&0.9049&0.9066&0.9082&0.9099&0.9115&0.9131&0.9147&0.9162&0.9177\\
1.4&0.9192&0.9207&0.9222&0.9236&0.9251&0.9265&0.9279&0.9292&0.9306&0.9319\\
1.5&0.9332&0.9345&0.9357&0.9370&0.9382&0.9394&0.9406&0.9418&0.9429&0.9441\\
1.6&0.9452&0.9463&0.9474&0.9484&0.9495&0.9505&0.9515&0.9525&0.9535&0.9545\\
1.7&0.9554&0.9564&0.9573&0.9582&0.9591&0.9599&0.9608&0.9616&0.9625&0.9633\\
1.8&0.9641&0.9649&0.9656&0.9664&0.9671&0.9678&0.9686&0.9693&0.9699&0.9706\\
1.9&0.9713&0.9719&0.9726&0.9732&0.9738&0.9744&0.9750&0.9756&0.9761&0.9767\\
2.0&0.9772&0.9778&0.9783&0.9788&0.9793&0.9798&0.9803&0.9808&0.9812&0.9817\\
2.1&0.9821&0.9826&0.9830&0.9834&0.9838&0.9842&0.9846&0.9850&0.9854&0.9857\\
2.2&0.9861&0.9864&0.9868&0.9871&0.9875&0.9878&0.9881&0.9884&0.9887&0.9890\\
2.3&0.9893&0.9896&0.9898&0.9901&0.9904&0.9906&0.9909&0.9911&0.9913&0.9916\\
2.4&0.9918&0.9920&0.9922&0.9925&0.9927&0.9929&0.9931&0.9932&0.9934&0.9936\\
2.5&0.9938&0.9940&0.9941&0.9943&0.9945&0.9946&0.9948&0.9949&0.9951&0.9952\\
2.6&0.9953&0.9955&0.9956&0.9957&0.9959&0.9960&0.9961&0.9962&0.9963&0.9964\\
2.7&0.9965&0.9966&0.9967&0.9968&0.9969&0.9970&0.9971&0.9972&0.9973&0.9974\\
2.8&0.9974&0.9975&0.9976&0.9977&0.9977&0.9978&0.9979&0.9979&0.9980&0.9981\\
2.9&0.9981&0.9982&0.9982&0.9983&0.9984&0.9984&0.9985&0.9985&0.9986&0.9986\\
3.0&0.9987&0.9987&0.9987&0.9988&0.9988&0.9989&0.9989&0.9989&0.9990&0.9990\\
\hline
\end{tabular}
\end{center}
\end{figure}
\begin{itemize}
\item In \texttt{R}: \texttt{pnorm(x)}
\end{itemize}
\pagebreak
\subsubsection{Quantilen der $\chi^2$-Verteilung}
\begin{figure}[h!]
\begin{center}
\scriptsize
\begin{tabular}{|r|rrr|rrr|rrr|}
\hline
\strut$k$&$p=0.01$&$p=0.05$&$p=0.1$&$p=0.25$&$p=0.5$&$p=0.75$&$p=0.9$&$p=0.95$&$p=0.99$\\
\hline
1&0.000&0.004&0.016&0.102&0.455&1.323&2.706&3.841&6.635\\
2&0.020&0.103&0.211&0.575&1.386&2.773&4.605&5.991&9.210\\
3&0.115&0.352&0.584&1.213&2.366&4.108&6.251&7.815&11.345\\
4&0.297&0.711&1.064&1.923&3.357&5.385&7.779&9.488&13.277\\
5&0.554&1.145&1.610&2.675&4.351&6.626&9.236&11.070&15.086\\
6&0.872&1.635&2.204&3.455&5.348&7.841&10.645&12.592&16.812\\
7&1.239&2.167&2.833&4.255&6.346&9.037&12.017&14.067&18.475\\
8&1.646&2.733&3.490&5.071&7.344&10.219&13.362&15.507&20.090\\
9&2.088&3.325&4.168&5.899&8.343&11.389&14.684&16.919&21.666\\
10&2.558&3.940&4.865&6.737&9.342&12.549&15.987&18.307&23.209\\
11&3.053&4.575&5.578&7.584&10.341&13.701&17.275&19.675&24.725\\
12&3.571&5.226&6.304&8.438&11.340&14.845&18.549&21.026&26.217\\
13&4.107&5.892&7.042&9.299&12.340&15.984&19.812&22.362&27.688\\
14&4.660&6.571&7.790&10.165&13.339&17.117&21.064&23.685&29.141\\
15&5.229&7.261&8.547&11.037&14.339&18.245&22.307&24.996&30.578\\
16&5.812&7.962&9.312&11.912&15.338&19.369&23.542&26.296&32.000\\
17&6.408&8.672&10.085&12.792&16.338&20.489&24.769&27.587&33.409\\
18&7.015&9.390&10.865&13.675&17.338&21.605&25.989&28.869&34.805\\
19&7.633&10.117&11.651&14.562&18.338&22.718&27.204&30.144&36.191\\
20&8.260&10.851&12.443&15.452&19.337&23.828&28.412&31.410&37.566\\
21&8.897&11.591&13.240&16.344&20.337&24.935&29.615&32.671&38.932\\
22&9.542&12.338&14.041&17.240&21.337&26.039&30.813&33.924&40.289\\
23&10.196&13.091&14.848&18.137&22.337&27.141&32.007&35.172&41.638\\
24&10.856&13.848&15.659&19.037&23.337&28.241&33.196&36.415&42.980\\
25&11.524&14.611&16.473&19.939&24.337&29.339&34.382&37.652&44.314\\
26&12.198&15.379&17.292&20.843&25.336&30.435&35.563&38.885&45.642\\
27&12.879&16.151&18.114&21.749&26.336&31.528&36.741&40.113&46.963\\
28&13.565&16.928&18.939&22.657&27.336&32.620&37.916&41.337&48.278\\
29&14.256&17.708&19.768&23.567&28.336&33.711&39.087&42.557&49.588\\
30&14.953&18.493&20.599&24.478&29.336&34.800&40.256&43.773&50.892\\
50&29.707&34.764&37.689&42.942&49.335&56.334&63.167&67.505&76.154\\
100&70.065&77.929&82.358&90.133&99.334&109.141&118.498&124.342&135.807\\
500&429.388&449.147&459.926&478.323&499.333&520.950&540.930&553.127&576.493\\
1000&898.912&927.594&943.133&969.484&999.333&1029.790&1057.724&1074.679&1106.969\\
\hline
\end{tabular}
\end{center}
\end{figure}
\begin{itemize}
\item $k$ = Freiheitsgrade = Anzahl Ausgänge - 1
\item $p = 1 - \alpha$
\item Wenn nichts anderes angegeben:
$\alpha = 0.05 \Rightarrow p = 0.95$ wählen.
\item Mit \texttt{TI-Nspire}: \texttt{inv$\chi^2$($p,k$)} bzw. \texttt{$\chi^2$Cdf($-\infty,x,k$)}
\end{itemize}
\pagebreak
\subsubsection{Quantilen für den Kolmogorov-Smirnov-Test}
\begin{figure}[h!]
\scriptsize
\begin{center}
\begin{tabular}{|r|rrr|rrr|rrr|}
\hline
$n$&$p=0.01$&$p=0.05$&$p=0.1$&$p=0.25$&$p=0.5$&$p=0.75$&$p=0.9$&$p=0.95$&$p=0.99$\\
\hline
1&0.01000&0.05000&0.10000&0.25000&0.50000&0.75000&0.90000&0.95000&0.99000\\
2&0.01400&0.06749&0.12955&0.29289&0.51764&0.70711&0.96700&1.09799&1.27279\\
3&0.01699&0.07919&0.14714&0.31117&0.51469&0.75394&0.97828&1.10166&1.35889\\
4&0.01943&0.08789&0.15899&0.32023&0.51104&0.76419&0.98531&1.13043&1.37774\\
5&0.02152&0.09471&0.16750&0.32490&0.52449&0.76741&0.99948&1.13916&1.40242\\
6&0.02336&0.10022&0.17385&0.32717&0.53193&0.77028&1.00520&1.14634&1.41435\\
7&0.02501&0.10479&0.17873&0.32804&0.53635&0.77552&1.00929&1.15373&1.42457\\
8&0.02650&0.10863&0.18256&0.32802&0.53916&0.77971&1.01346&1.15859&1.43272\\
9&0.02786&0.11191&0.18560&0.32745&0.54109&0.78246&1.01731&1.16239&1.43878\\
10&0.02912&0.11473&0.18803&0.32975&0.54258&0.78454&1.02016&1.16582&1.44397\\
11&0.03028&0.11718&0.19000&0.33304&0.54390&0.78633&1.02249&1.16885&1.44837\\
12&0.03137&0.11933&0.19160&0.33570&0.54527&0.78802&1.02458&1.17139&1.45207\\
13&0.03239&0.12123&0.19291&0.33789&0.54682&0.78966&1.02649&1.17357&1.45527\\
14&0.03334&0.12290&0.19396&0.33970&0.54856&0.79122&1.02823&1.17552&1.45810\\
15&0.03424&0.12439&0.19482&0.34122&0.55002&0.79259&1.02977&1.17728&1.46060\\
16&0.03509&0.12573&0.19552&0.34250&0.55123&0.79377&1.03113&1.17888&1.46283\\
17&0.03589&0.12692&0.19607&0.34360&0.55228&0.79482&1.03237&1.18032&1.46483\\
18&0.03665&0.12799&0.19650&0.34454&0.55319&0.79578&1.03351&1.18162&1.46664\\
19&0.03738&0.12895&0.19684&0.34535&0.55400&0.79667&1.03457&1.18282&1.46830\\
20&0.03807&0.12982&0.19709&0.34607&0.55475&0.79752&1.03555&1.18392&1.46981\\
30&0.04354&0.13510&0.20063&0.35087&0.56047&0.80362&1.04243&1.19164&1.48009\\
50&0.05005&0.13755&0.20794&0.35713&0.56644&0.80988&1.04933&1.19921&1.48969\\
100&0.05698&0.14472&0.21370&0.36331&0.57269&0.81634&1.05627&1.20666&1.49864\\
200&0.06049&0.14887&0.21816&0.36784&0.57725&0.82099&1.06117&1.21180&1.50458\\
\hline
\end{tabular}
\end{center}
\end{figure}
\begin{itemize}
\item Werte entsprechen $k_{\text{Krint}}$
\item $p = 1 - \alpha$
\end{itemize}
\pagebreak
\subsubsection{Quantilen der t-Verteilung}
\begin{figure}[h!]
\scriptsize
\begin{center}
\begin{tabular}{|r|rrrrrrr|}
\hline
$k$&0.75&0.8&0.9&0.95&0.975&0.99&0.995\\
\hline
1&1.0000&1.3764&3.0777&6.3138&12.7062&31.8205&63.6567\\
2&0.8165&1.0607&1.8856&2.9200&4.3027&6.9646&9.9248\\
3&0.7649&0.9785&1.6377&2.3534&3.1824&4.5407&5.8409\\
4&0.7407&0.9410&1.5332&2.1318&2.7764&3.7469&4.6041\\
5&0.7267&0.9195&1.4759&2.0150&2.5706&3.3649&4.0321\\
6&0.7176&0.9057&1.4398&1.9432&2.4469&3.1427&3.7074\\
7&0.7111&0.8960&1.4149&1.8946&2.3646&2.9980&3.4995\\
8&0.7064&0.8889&1.3968&1.8595&2.3060&2.8965&3.3554\\
9&0.7027&0.8834&1.3830&1.8331&2.2622&2.8214&3.2498\\
10&0.6998&0.8791&1.3722&1.8125&2.2281&2.7638&3.1693\\
11&0.6974&0.8755&1.3634&1.7959&2.2010&2.7181&3.1058\\
12&0.6955&0.8726&1.3562&1.7823&2.1788&2.6810&3.0545\\
13&0.6938&0.8702&1.3502&1.7709&2.1604&2.6503&3.0123\\
14&0.6924&0.8681&1.3450&1.7613&2.1448&2.6245&2.9768\\
15&0.6912&0.8662&1.3406&1.7531&2.1314&2.6025&2.9467\\
16&0.6901&0.8647&1.3368&1.7459&2.1199&2.5835&2.9208\\
17&0.6892&0.8633&1.3334&1.7396&2.1098&2.5669&2.8982\\
18&0.6884&0.8620&1.3304&1.7341&2.1009&2.5524&2.8784\\
19&0.6876&0.8610&1.3277&1.7291&2.0930&2.5395&2.8609\\
20&0.6870&0.8600&1.3253&1.7247&2.0860&2.5280&2.8453\\
21&0.6864&0.8591&1.3232&1.7207&2.0796&2.5176&2.8314\\
22&0.6858&0.8583&1.3212&1.7171&2.0739&2.5083&2.8188\\
23&0.6853&0.8575&1.3195&1.7139&2.0687&2.4999&2.8073\\
24&0.6848&0.8569&1.3178&1.7109&2.0639&2.4922&2.7969\\
25&0.6844&0.8562&1.3163&1.7081&2.0595&2.4851&2.7874\\
26&0.6840&0.8557&1.3150&1.7056&2.0555&2.4786&2.7787\\
27&0.6837&0.8551&1.3137&1.7033&2.0518&2.4727&2.7707\\
28&0.6834&0.8546&1.3125&1.7011&2.0484&2.4671&2.7633\\
29&0.6830&0.8542&1.3114&1.6991&2.0452&2.4620&2.7564\\
30&0.6828&0.8538&1.3104&1.6973&2.0423&2.4573&2.7500\\
50&0.6794&0.8489&1.2987&1.6759&2.0086&2.4033&2.6778\\
100&0.6770&0.8452&1.2901&1.6602&1.9840&2.3642&2.6259\\
500&0.6750&0.8423&1.2832&1.6479&1.9647&2.3338&2.5857\\
$10^3$&0.6747&0.8420&1.2824&1.6464&1.9623&2.3301&2.5808\\
$10^4$&0.6745&0.8417&1.2816&1.6450&1.9602&2.3267&2.5763\\
$10^5$&0.6745&0.8416&1.2816&1.6449&1.9600&2.3264&2.5759\\
$10^6$&0.6745&0.8416&1.2816&1.6449&1.9600&2.3264&2.5758\\
\hline
\end{tabular}
\end{center}
\end{figure}
\begin{itemize}
\item Freiheitsgrade: $k = n + m - 2$
\item Mit \texttt{TI-Nspire}: \texttt{invt($p,k$)} bzw. \texttt{tCdf($-\infty,x,k$)}
\end{itemize}