\begin{methode*2}[Prendre une décision\MethodeRefExercice*{2SP2_E_prise_decision}]
\label{2SP2_M_prise_decision}
Dans les conditions de la définition et de la propriété: 
\begin{itemize}
\item On émet une hypothèse sur la proportion du caractère de la population $p$.
\item On détermine l'intervalle de fluctuation au seuil de \upc{95} de
la proportion $p$ dans des échantillons de taille $n$.
\begin{itemize}
\item Si $f_o$ n'appartient pas à cet intervalle,\\ on rejette l'hypothèse faite sur $p$ \textbf{avec un risque d'erreur de 5\%}.

\item Si $f_o$ appartient à cet intervalle, on ne rejette pas 
l'hypothèse faites sur $p$.
\end{itemize}

\end{itemize}
\exercice

 Dans la réserve indienne d'Aamjiwnaag, située au 
 canada, à proximité d'industries chimiques, il est né 
 entre 1999 et 2003, 132 enfants  dont 46 garçons. Est ce normal?

      \correction
        On fait ici l'hypothèse $P$ suivante : \og le sexe d'un enfant qui nait 
        dans cette réserve est un garçon avec une probabilité de 0,5\fg.\\
        La taille de l'échantillon est $n=132$ ($n\geqslant 25$) et\\ la fréquence 
        observée est         
    $f_o=\dfrac{\TopStrut 46}{\BotStrut 132}\approx0,34$ \\avec $0,2\leqslant f_o \leqslant 0,8$.\\
        L'intervalle de fluctuation au seuil de \upc{95} est: \par $IF=\left[0,5
        -\dfrac{\TopStrut 1}{\BotStrut \sqrt{132}};0,5+\dfrac{1}{\sqrt{132}}\right] 
        \approx[0,41;0,58]$.\par
        $f_o\notin IF$ et on rejette l'hypothèse $P$.\\
        La probabilité qu'un garçon naisse dans cette réserve n'est pas de 0,5.
\end{methode*2}


\begin{multicols}{2}
Les 95\% sont illustrés avec le graphique qui suit :\\
On simule 100 fois le comptage de garçons sur 132 naissances.
Dans 94 simulations, la proportion des garçons nés se trouve 
dans l'intervalle de fluctuation.

\columnbreak 

\begin{center}
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\end{multicols}

