From 20a5163b7fc576a391f4983c15cee1db69c0909e Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Tue, 15 Nov 2022 08:02:45 +0100 Subject: [PATCH] Feat: import 2e seq pour l'enseignement scientifique --- .../02_Biodiversite_et_evolution/1E_CMR.pdf | Bin 0 -> 178348 bytes .../1E_simulation_CMR.pdf | Bin 0 -> 52026 bytes .../1E_simulation_CMR.tex | 53 ++ .../2E_confiance.pdf | Bin 0 -> 43579 bytes .../2E_confiance.tex | 93 ++++ .../2E_confiance_simulation.pdf | Bin 0 -> 91793 bytes .../2E_confiance_simulation.tex | 33 ++ .../3E_Hardy_Weinberg.pdf | Bin 0 -> 70362 bytes .../3E_Hardy_Weinberg.tex | 161 ++++++ .../exercises.tex | 7 + .../fig/bas_tableur.png | Bin 0 -> 11668 bytes .../fig/confiance.pdf | Bin 0 -> 16046 bytes .../fig/confiance.svg | 484 ++++++++++++++++++ .../fig/confiance_tableur.png | Bin 0 -> 77327 bytes .../fig/haut_tableur.png | Bin 0 -> 22542 bytes .../02_Biodiversite_et_evolution/index.rst | 42 ++ Enseignement_Scientifique/index.rst | 3 +- 17 files changed, 875 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+\begin{exercise}[subtitle={Simulation de la méthode CMR}, step={2}, origin={Création}, topics={Biodiversité et évolution}, tags={Échantillonnage, Statistique, Tableur}] + Dans cette activité, nous allons simuler avec le tableur la re-capture d'une population marquée pour voir la fluctuation de cette méthode de comptage. + + Pour cela, on va imaginer une population de 500 individus que l'on va chercher à estimer en faisant un marquage de 100 individus puis en re-capturant 50. + + \noindent + \begin{minipage}{0.7\textwidth} + \begin{enumerate} + \item Reproduire le tableur ci-contre en complétant les cases jaunes avec les données de l'énoncé. + \item On commence commence par simuler une seule re-capture. + \begin{enumerate} + \item Quelle est la probabilité d'un individus capturé soit marqué? Compléter la case verte du tableau. On note dans la suite cette probabilité $p$. + \item Pour simuler le fait qu'un individu re-capturé soir marqué ou non, on utiliser la formule suivante: \calc{=Si(ALEA() < p; 1; 0)} où $p$ est à remplacer par la valeur trouvée à la questions précédente. Compléter votre tableau pour simuler 50 re-captures. + \item Calculer le nombre d'individus marqué puis estimer la population avec la méthode CMR. + \end{enumerate} + En appuyant sur la touche \texttt{F9}, la simulation (tous les \texttt{ALEA()}) sera rejouée. + \item Repoduire ce qui a été fait avant pour simuler 50 re-captures. + \end{enumerate} + \end{minipage} + \hfill + \begin{minipage}{0.25\textwidth} + \includegraphics[scale=0.3]{./fig/haut_tableur} + + ... + + \includegraphics[scale=0.3]{./fig/bas_tableur} + \end{minipage} + + \begin{enumerate} + \setcounter{enumi}{3} + \item Tracer un graphique représentant les populations estimées lors de vos 50 simulations. Décrire les valeurs obtenus. Que peut-on en conclure sur la précision de la méthode CMR? + \item Changer les paramètres \texttt{Population totale} et \texttt{Individus marqués} puis décrire le comportement des simulations. Dans quelles conditions, la méthode CMR donne de bons résultats? De mauvais résultats? + \end{enumerate} +\end{exercise} + +\vfill + +\printexercise{exercise}{1} +\vfill + +\end{document} diff --git a/Enseignement_Scientifique/02_Biodiversite_et_evolution/2E_confiance.pdf b/Enseignement_Scientifique/02_Biodiversite_et_evolution/2E_confiance.pdf new file mode 100644 index 0000000000000000000000000000000000000000..212f1c4c4a1fee7c7e724bc621184461726400ef GIT binary patch literal 43579 zcmce;19T=`);64^<8*A>ykpz8ZQHid>DcPnopfy5?%1}vqc3@$d1mJQ-udTS>tAc; zzSpT!2X(ObslDr5dsmUl3yabM=vbgh$L71|`j@8q2B4V<7zpePEup!&3FwtQ>`e&h z)#VH=O^log=#^Xyo&U%YwR5x~p#M1jQ3F6gFDPi|PN4OEDFXq3;m@E$Krdt9>}c_k z5BRg>kK=p3qKT88i=&Z=69LP6mg0L;7S_%tj_v8mxYu8&J5w4Ox+924?2rWJz zJs*z)U0h~wno}iw;Eox?qwZEt{{zyS?5{~2JkmbAmM74q6fvxk&Pk(*ycd0<=H5ws zKLV?n1%ILB7^IQ8#io*9YE5MaaqyjSqcsyu7jxG~H$vu%BY+tE0AT3-I6vA>Zf}A* zM+*UB3CdvDZ-uV1MH&Zsh#K46qFAZnGn!$&85A;Tq$B`Agv!xv$ef%TD-^dwwcrv0 zD8^U5+uK{UWe#H=eTLDfFXIqMs zbF9%^IfXIh>_Cd&GWqmLhxF47C$HvOBo5#_ns;fO%nR$o6VqKMg;#8sx|87i6?ieBZ)OcjjerEs8;f&Y 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+\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} +\usepackage{wasysym} + +\author{Benjamin Bertrand} +\title{Intervalle de confiance} +\date{novembre 2022} +\tribe{Enseignements Scientifiques} + +\pagestyle{empty} + +\setlength{\columnseprule}{0pt} +\setlength\columnsep{5pt} + +\geometry{left=10mm,right=10mm, top=5mm, bottom=5mm} + +\begin{document} + +\maketitle + +\vfill + +\begin{bclogo}[barre=none, arrondi=0.1, logo=]{Cours: Intervalle de confiance} + \begin{minipage}{0.6\linewidth} + On cherche à estimer $p$ la proportion d'un caractère d'une population. Pour cela, on fait un échantillon de $n$ individus de cette population et l'on calcule $f$ la fréquence (proportion) du caractère dans cet échantillon. + + On peut définir \textbf{l'intervalle de confiance à 95\%} + \[ + IC_{95\%} = \intFF{f - \frac{1}{\sqrt{n}}}{f+\frac{1}{\sqrt{n}}} + \] + Alors $p$ est dans cet intervalle avec une probabilité de 95\%. + \end{minipage} + \hfill + \begin{minipage}{0.3\linewidth} + \includegraphics[scale=0.6]{./fig/confiance} + \end{minipage} +\end{bclogo} + +\vfill + +\begin{doc}{Sondage d'élection} + Deux candidats se présentent à une élection. Un sondage est commandé pour chercher à prédire les résultats. Il est fait sur 1302 électeurs. 629 déclarent qu'ils projettent de voter pour le candidat A et le reste pour le candidat B. + \medskip + + \begin{enumerate} + \item Calculer la proportion de personnes qui annoncent vouloir voter pour le candidat A. + \item Calculer L'intervalle de confiance à 95\% associé à ce sondage. + \item Peut-on affirmer que le candidat $A$ a aucune chance d'être élu ? + \end{enumerate} +\end{doc} + +\begin{doc}{Compétition entre établissements} + Trois établissements scolaires revendiquent être les meilleurs pour préparer leurs élèves au bac. Voici leurs résultats pour l'année dernière. + + \begin{center} + \begin{tabular}{|c|c|c|} + \hline + Nombre d'élèves & Reçut & Refusé \\ + \hline + Lycée A & 40 & 13 \\ + \hline + Lycée B & 87 & 36 \\ + \hline + Lycée C & 140 & 16 \\ + \hline + \end{tabular} + \end{center} + + \medskip + Peut-on affirmer qu'un établissement est meilleur qu'un autre ? +\end{doc} + +\begin{doc}{Deux phénotypes de l’épervier strié} + % Issu du livre scolaire + L’épervier strié est un poisson qui vit dans les récifs coralliens. Il existe sous deux phénotypes : sombre et clair. Un recensement des formes claires et sombres a été effectué le long de cinquante-quatre transects, de la surface jusqu’au fond du lagon. + + \begin{center} + \begin{tabular}{|p{2cm}|p{2cm}|p{2cm}|} + \hline + Nombre de Poissons & Profondeur < 5m & Profondeur > 5m \\ + \hline + Sombre & 538 & 20 \\ + \hline + Clairs & 310 & 238 \\ + \hline + \end{tabular} + \end{center} + + \medskip + Peut-on affirmer que les poissons sombres préfèrent vivre proche de la surface ? Qu'en est-il des poissons clairs ? +\end{doc} + +\end{document} diff --git a/Enseignement_Scientifique/02_Biodiversite_et_evolution/2E_confiance_simulation.pdf b/Enseignement_Scientifique/02_Biodiversite_et_evolution/2E_confiance_simulation.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0778fced4235f298305bf56f87ac42ac05fd2250 GIT binary patch literal 91793 zcmd431z6SV);$Uc28eT4XrWGB5xYHeVK z$;XGutmOREh?H4P*1*ij&<>MX(cZxB>?dN@HkO#oLPFL~q?-5Od6s);|7c?}BY$)D zDi%y;X?;5zQ+R>}o`ByY{|!$l7};9e+ZYCTcDIkDpYiDDmZ;9#jz4z)jIht=j&`>TMqpo2ZSt0)T4g4Q+ z=v?r||CuRp|GTEZ^BE74%kTXCe^1}bx3#U`iLH&* zp^0Xqg{iONw{7%fK7L0dPoLtioDs0;b#+PZnb*~)y+;S%Rv3sz^{bwRr)Dx;9X4`s zbf`6PaO=bv2h>e@M zBkFPSUtF4|d_li#X|uX9hp$#YlJJf=p6^vnz}WM)xOPB~Q*Ja;xxF7ty zl|N2x8P;RmyOlqrd-EJU%O)}L-GE4TA=S^#Hn)}=+a#ZE&JQbbDdA+Mr0KtCd&sjo zuE_knMD?kdm)L1O@8F#aFHP@!soomDtS47{4s#nU1}ehqFOOB-1jtoy)@);*dvN7<`^_r zUb_^Z)BY)o@z zr+CtxvLrrn%gghj2V|DF^q!p5+cMp4RKMo_>WK;7XYN~(xALz=gdteE71|rOzIR!m 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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/Enseignement_Scientifique/02_Biodiversite_et_evolution/3E_Hardy_Weinberg.pdf b/Enseignement_Scientifique/02_Biodiversite_et_evolution/3E_Hardy_Weinberg.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b3c1908499397696721ece33e2b237501809d859 GIT binary patch literal 70362 zcmce;W2|t^wk5o6+qP}{*|u%_*|u%lwr$(CZL{BV``$18qm!@yoU@X(QkYe#kuft< zRdZyK%8Q86GSaa^kaD0(3wJ2wI?hJWlC8UE|lfujFc&wq_#grb)*aCWr#$Aa-6i+}q6_5H^}(ZtE_ zucMKP69MZ#Es9X|(k8ZM&gKM+tOWo4{4DfwPH-iIJVL2^1e6l#{cg ziGdB2+r}dNj6B869uNTdH{czViLLQ}_xw}(*V5VlnfN~gf#cr=f%88Gf$?AD{99;X z{1@f_86Fs!{%s)sbI!#0Z}TRme{uYuVS?#jr2kvoiHZ3?2jX8r@ZST1?LPExzP*o;%Xe|eY6&d>M0*h#+I9Z;kn%qSGQ(L?d8Q9k$qBa=+o*_%8XTZDWhL9GgV(@`q zfXCDR_+^m_nPhRkWWRg33bajio@yvRX<0?Y1Vo~KMblgg9i$R{s?GKm&1I)Yy9Fe% 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