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2020} +\tribe{Enseignements Scientifiques} + +\newcommand\cours{% +\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} +} + +\begin{document} + +\cours +\cours +\cours +\cours +\cours + + +\end{document} diff --git a/EnsSci/02_Biodiversite_et_evolution/4E_confiance.pdf b/EnsSci/02_Biodiversite_et_evolution/4E_confiance.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cc05f73f4e5085cfe2487c995a89a01520aa92a0 GIT binary patch literal 32962 zcmce;bBriY*DXA@XU^ER?U^&SZQHhO+qP|c=8SFI#y!6m-}ff>CinjHJe_o>x@uQ- zudJP&s=X>jA}1t5!$8XdMKZTIyb8sPPmgbFU;)L=4MnHqZfA^7rzUG)VQlCGMW^U& z;Pf9gBDN0JP;`QVwr=>E^ndLc=>Ox^hNAnY?|EnNy{M#Tf{6o&a zga(FxDF65Hz`*z~1M%;3CWe2RH!=Rh@xO-&#(zlvm$(xn)4vbIKSA(c1A_J62jU;k z{g;4X`kzevSNLXRWn%o#`2Bwm-&dMju^X&NzB|2wwp75TDLZ(>dvM|#&>ASAq-&j? zX79UW>q5aaHyX<=UpKa|6cZ`g>=!6zbz*fzB8O9UA%~yrO?G!ReZ!GdUAlw=uqL1) z0nk9fB~o<;(6*&JT^{yNpU3BwzTygUQAI@sZS6E=B2klqV!`yK!_y6~?Vmkc(-5>5 zSAz!46{e0AV(l=-&E`9LQfSsJiN-u1N5`R3MES%k_;QQ`MwHnS3$^^EH#RlbwfvH= zq6w^m_*KU8)wR^w;t|ZqprToQ5EuK;=f{?={f`*+ddXju7_(Zp|^8VJzsNp;U4Y{BTI_l#Co`5g5llR3wG3rs6M< z2ar3*g|OcyI<#8uU@~(h&M3;K{-{XfaY1ULfj5X`ZwX0JNMC<(IzAW6{CF|dldcV} zv3l5GL9H9|cHPPwgJNd;qtJO1U+3SxMOCSKVPGrEjf73K!x6ZZg-Kp4k^wQfY5PUE z@%}feZ@oa^fP~bA6A0E2zAG~;7(x0{+`95Aw)J*z zHSe%N#=ZU+QN_)evuZcv($!qb-!BM>B%HR!SI(pXF$m+rxevNgZ80+b@?3b6!%13u z%%5zy_HDfz$%vi1TWtf=49ef?ZY@}!zK-Rp1W+yb#AK%j?rMM-aZpFg3}3|xPY}zbN8yUo zevH2&=jH`8y_j0#!1BX@x!_?#8t@tYRmE<5UnP>9Ig_lLHKTjs1|*DBuiXO9QP7l13=14G0XdAPCa!L+^G z1gM8r41>7t{A3RN^8vb!1BZuC^TcIw0K=pQV% zZ_kwKH_gFS4K{@W9QKt4d9X=TcQbD{;=v=ea=>&0)Uc2>9y}N(E0rNB7QH=F9D+R8 z)H;jmacZq6Alvww*P4zPhTwo`3mmXZicQ>GUw=J>>j>FCzR<2Ga%(TED`fHLM4K!# zU3+@|P>kD_fdOF{lyh*Nct_l@RJVqR7zoTC-?1~@MsWhy4|yCvMvxcg1+y58{s72L zP(+8>Sy7bEqUDpP<%x=_cyO+1j}GveEZ zFf?Yu>=7e&nbl&L6okch)+VGNB2Ozv$^8xK zC2+YaF>$XuXE99mx@!whJ8s#o>KYmij9fmytQkB!FY|MJ_}UjBp_w65@~z2w@h;m*Cw* zAoTuN8xfY@-E7TOEDe;SDA=ImA2>Ijm)v45VVW4<$^!WGE_c@NrS?a`XWGH0t<8`{ zoddUe3^eNfY_(~N9mA$i#2P$fzaauFhAM7xXF*`6IfP?HPJ_a&V&|0Bae&L2SXrz% za{&#rV24OqA^Wk70=nV-nX~r~yy^puA;x?dJ6;RI4s4R@pbnV#PBw9U;@z(BU>gcz z!a)kMhke8YZwMX!aA#-(iNhrY$NRPehw9KjT1~m%7d-NY&|Gq^to7w#i~SHBuhgtJvoh&(>_BI`*_j`m0%LU}wZ^2z*NzJJX`YN{oDCSTd5O8`2>vi_}l! 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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 + + Peut-on affirmer que le candidat $A$ a aucune chance d'être élu? +\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{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} + + \medskip + Peut-on affirmer qu'un établissement est meilleur qu'un autre? +\end{doc} + +\end{document} diff --git a/EnsSci/02_Biodiversite_et_evolution/fig/confiance.pdf b/EnsSci/02_Biodiversite_et_evolution/fig/confiance.pdf new file mode 100644 index 0000000000000000000000000000000000000000..bd4b3dbfd5914a410ec8e307507175f498836b80 GIT binary patch literal 16046 zcmd731z23o(k_}1AV7k<55au~cXxLuI1KJC!CgYo5S*Y176=gB9fDhM3GNaS?9RZK zz4Pt8|NlSd-g}ASQMs%Fp{{S4eCCAi&<(3W<*o zz$|BGXW;?{utP{HNB{tUS;ErB#mouvv@voq6EichH#I{N5I}NvaWXTqMe<1B&>XPS z<9xobOJ6M)pfhz<$*6=yqXe*Rl5N1F$?Oc^cYA~Q>xw^7O8;vHQ@tG~g*!^Q6tRlW z7LV=mkM0#g&5XWD$!V8YDp`{jzE>9x0!y#Bw{O*#noVy$XPxc0?VuW9C*u>Q*)0aI zo+aP}oX)ak8I`7vl(^BR;SjG6dl=vx@KBnls(wSl)L%GzYJ8euL|0Hhm^R0$y8r1T z?2pf!&w>f84~yJyj_2Ox{ZgMrPh0ZSVR}bk9IJg7qA9qxM16jsXd5$ms6NrM^>q$8 z=BJ>@C28E~p^ov{M$qkw0=EUh%}O*zVuJKg&5kSUFgCE!Tcx&#&|5U8p0|Y4KFgq) zpJW*IE48nm04d2~OT(2Iefr0`$3OK{Wzzg8eSf@c@*G7iy!GMny?U92iW(R9BT)Kh z53j4YgA16+D}hA>P5^|lPkHRXF2R?8*d}@q9VN|67{mC?P2ce-dDx$FT`5A=0AN2N zJ~D;~-xX|YDl6lkVVyA{N^2iWX8{?~_%U7_Q zzj`{hqpy7h_Nx|~`!DiHzWA0Oe*M+i!aZ6_JDW^UjA>?I>{RX-U?Smfk|Sw{MbtJ6 zi=|eBwx%rChEEL?A2$rXctYK1@zKR55#eK>VcI@SP$k$fH!MKqlj` z^Y+-!17a>Zo%PJe+f&{di|x7ubYpikbEHfsq;9>$Af0Xa0e29fNh`d`LkD+InXQF+?4Tu^(Oeh* zp2>X88e>K>zD{dW2d#v*l)*LBrrACahMjsxttKB1R1VRS76!EXkA8iAmv!z40?Cob z2`-|k^GC|CTB72rN=FD$RpGM!sDLG#mvwQU0+l~A3d6^E_Ts<}6aS(T;uW#1Xto>m zAT)hKS;vfI{TS2qT=r?`JMXM5nqr161VjGlJgmoQQ+PKBFDPXY@Q%PWQtfJ|?Jj9u zonn6dZ}4LBs3@s$NW9PF{bvt~K?=|EggJ31Yx=OF$;}8DwAs2k^GQ#Y+{=j72guJe zN(;>B)X}-H_;~QkP+U<$H6qJgUGM`^>Cwesctpb@<IUw_905iG`Ls0$r~Qjjx^v>I-D!4(w(`IPL!JDYFjenRX- zA9wRB(n@%zI%=E9C9y|Gx9PsgeOzZWv2e_h-a5l!&Enxl8k8Vr(P`AJ*cA#gZt6kI z4vFJtnZ*Be-t2(CkeajtVmGPbNB`38eQHg{qt0xZVDBwC;>gENR`P|T07oZQYKssM z{cP$Q;qjG>ejqQs34zfB{$x!%-0fZ}JnRX|P15_L^N8osPj&L=YEogEH;^$HX0@t9 zGH~-&^gP|vX3I73$TRjavf+5-)Tspi=?Ux#GnKC_@D&H zhuH`S2>_Tyg#jP{vxyPp4l(n;<3PXTfJ`jx>}(*``y~GeJfwWMGb|b8UAZP;~>h+g=@2m6B zaFKtu5d;JR0r$6uc4?`)m^s`Npd~YF|2?Q?X=7<;@dqa*BTGA%Kf>}xE>4#B@?&D* zVrAoisuvKz2BJg8b}DH>aunLzsd z;D)vaA_%A~AiuwK_&!R^9)R@kdVSyizZ9GMw?06*{HvUxI`Uu7T%a;|=*Pb*bT1WE zS7VoZb&{}mvc0GLHxm74yFd?`_Rsozq}%F9mz~uiFYaPB3(cp6nXDrO_*>cEic|l1 z+OC~ka)e{1vMM=-@wD%dbd&k|>Tqe=;O=;O>CU+_q#@Sv+~MX+G@kq3MkM=E-lp{g zeXIlZMRhkldGGx?--2-a1MDuNN zWU@zh8u-6{c!YC+yTWD2pzMV+(x zGpL(RX6~u;NY6c8*=zaOxS%H3{%a}ixqnf^n=f1yL%pJ**-Zn?5}!NIMLJPdQZtZ1 z3Y1?_4*@vNZN5xx$d$d-rU~ghPm{zP6mDN)!E3J9A-vIan(6Ey^g+s?_)z4qV}JCX z)+){I-D}R{#vnn1=2kBeC0J5gPa_us;umBo1cwutW(?Uf$)m!f`j5(ksB(?a$H>wb zm&d__X0zEtl9S4PAUU;jMWSTo){(G)3+egdb?~`7Il;|if*f)$!YQr2ETb*sD?T%04aH0zI zslshvH0#FRW;FZg1<|bjNX~b{dpZX9{S$nE_#t`~;vg89&=WS1g=Bv0h4kTqxE-v_ z5|bc|5ztg#3s30owoU!fRP)4XMlO$jGM(8_p^POcMa1>y~^V)%gp zDtxmU=3dd*JaW2*t#~@gU0NtxIJt!`kp$s{plFifq0uhlou1No`>YUlG0_oAO)*)*)3Os zkvaEy$m~}=p(8bbn2*549@(8qAf{a!ZjtKNTLA2PB8`hKpzyCsBzv_jyzm z7&=&0)B1)1brJ`=q_uev1G6cHZNsf1O1k#YVrOa53aRH6(-)2Qgr2X$McAK3jgk}f zGQMT;e7}Su86%|2cUm`sC%i#2qdb%7AQTL>E`-G5*f3xbhXQdtHNhE_jiLoHZbHTGdlfd*$E=}L`cA;vq4!rBl5gAmrVw%(PYbeTmMB2`%g3`sC7IdL1sIy z4k+whd}~K?5azH1%|63B{{>s+(XXLf^rz)TM?=B^?SKysS~;9St}s0z-OcSL!FBBU zL}+Hv{{H%*2QBe~VW_T7qop#m&vC>3=sf*AemE8%5i5tVJ~@qkQYga4*{1NG3U(Ng zi=47KLdEMPqFH6yw?q%2PW?U~N0_(tXofoGaq_Z2MyoJ~Lb@Ft+tyZC z-?iQ$b=<;o9D{zh)ced6JC2`h1NHQQ~sw>|-8n6rxsDx9e2<*eDbg z@JXgN^qXvTlWJiXc5$5m!Oj`nihs*8d1< zo44*MF`Mmr|E8ms8k&q4^Nr zQbBplKF(Z5^6CSbo#zmfM`me^W^@hK`3IgR1gVHmQm`@ew~!ITrH@~UH1*zX2RW?_ zVf^h?o6Zx?7nJ=2-Mqs2%lvJ8JCvzG>JFHS5S#9@?l%#<22TQK#k9|pW4G!G9jk4J zI`Ini>4Xu1H#)RAecDux-v^6lSr@N*$wIg<<##CwaJNj62t|JJ0E}HbI$9Jk4j-17mhBw4V(dmMNEKw&<>!XtkZ?#kc! 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