From 94c57e58d56246baedc9f9867ac55ea77781cecf Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Mon, 13 Dec 2021 09:40:53 +0100 Subject: [PATCH] Feat: simulation de l'intervalle de confiance --- .../3E_confiance_simulation.pdf | Bin 0 -> 91793 bytes .../3E_confiance_simulation.tex | 33 ++++++++++++++++++ .../fig/confiance_tableur.png | Bin 0 -> 77327 bytes .../02_Biodiversite_evolution/index.rst | 10 ++++-- 4 files changed, 40 insertions(+), 3 deletions(-) create mode 100644 EnseignementsScientifique/02_Biodiversite_evolution/3E_confiance_simulation.pdf create mode 100644 EnseignementsScientifique/02_Biodiversite_evolution/3E_confiance_simulation.tex create mode 100644 EnseignementsScientifique/02_Biodiversite_evolution/fig/confiance_tableur.png diff --git a/EnseignementsScientifique/02_Biodiversite_evolution/3E_confiance_simulation.pdf b/EnseignementsScientifique/02_Biodiversite_evolution/3E_confiance_simulation.pdf new file mode 100644 index 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+\tribe{Enseignements Scientifiques} + + +\begin{document} + +\begin{exercise}[subtitle={Simulation des intervalles de confiance}, step={2}, origin={Création}, topics={Biodiversité et évolution}, tags={Échantillonnage, Statistique, Tableur}] + À la manière de la simulation avec le tableur réalisé sur la méthode CMR, nous allons simuler plusieurs sondages pour construire des intervalles de confiance. Le but étant d'expérimenter le \textit{niveau de confiance à 95\%}. + + Pour réaliser cette simulation, nous allons fixer une valeur de $p$ que nous supposerons inconnue. Puis nous allons simuler plusieurs sondages de taille $n$ pour calculer l'intervalle de confiance associé. Enfin nous calculerons ne nombre d'intervalles de confiance qui contiennent $p$. + + \begin{enumerate} + \item Reproduire le tableur ci-dessous. Commencez par remplir les cases en rouge qui sont les paramètres, puis simuler les individus du premier sondage, calculer le \textit{Total}, \textit{Proportion f}, \textit{borne inf} et \textit{borne sup} puis reproduire ce sondage 100 fois. + \begin{center} + \includegraphics[scale=0.2]{./fig/confiance_tableur} + \end{center} + \item Représenter graphiquement les lignes \textit{Proportion}, \textit{Borne Inf} et \textif{Borne sup}. Vous pourrez utiliser le type de diagramme "cours > diagramme des cours 3". + \item Ajouter une case où vous compterez le nombre de sondages où la proportion $p$ est comprise dans l'intervalle de confiance. + \item Y a-t-il beaucoup d'intervalles de confiance qui ne contiennent pas la proportion $p$? Faire varier la valeur de $p$pour vérifier si cette observation dépend de cette valeur. + \end{enumerate} +\end{exercise} + +\vfill + +\printexercise{exercise}{1} +\vfill + +\end{document} diff --git a/EnseignementsScientifique/02_Biodiversite_evolution/fig/confiance_tableur.png b/EnseignementsScientifique/02_Biodiversite_evolution/fig/confiance_tableur.png new file mode 100644 index 0000000000000000000000000000000000000000..3c213b34ae5e289532822c2221bc9b5eaf1d3cee GIT binary patch literal 77327 zcmc$`1z45q);2m7W1&k~Dh4W{OuD3{F^EYw(jpDgB}kbVz zhqYX5@ALor`@a92b6tmPUwdzL&X@OnpYe=wkNdvI^HNSm?8LE)$1oVo37q(C1q|kh zE(UW@^|vGNH)cdXoZx>B+1|t{{RTfSzv;h#Ka<#r+_6)%G_-TnwK2dLSy-AIFxl$a z7#LXC8e7^e5L60cFccWv?HfuDB4-C2?UXuuYZiy%J%cYuOunIg^pY`Zp?=;49Mh5P#RXIRc6^W?8TV1^xTpGJ?e|MQ-ZUz1eW z;q;j^oL9c5rhUR--WxQ3CRhAv)}%>#L~asGO`WP=htE7oKx=p1(WC!c{{b6M+oQFl z%~2np_+R^V8H|kZzg|=Pq{Q&O5-+!Q?AS9qrB(rGq6D#M)i7RyGT(+~nj*+|T zveGKXYcu*{cX!J&ir-1$;o59#o=Lk>se`$y=MmxugM)(?1zn1|vUIWnXk@1+TjMsT 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