<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/3c05a2a6-d21e-444d-ad65-e0025fe4005e/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1a wsc"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1a wsc">1 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls1a wsc"> </div></div><div class="t m0 x1 h4 y5 ff2 fs1 fc1 sc0 ls1a wsc">Estatística Aplicada - Resumo </div><div class="t m0 x1 h4 y6 ff2 fs1 fc1 sc0 ls1a wsc"> </div><div class="t m0 x1 h5 y7 ff3 fs2 fc0 sc0 ls1a wsc">DISTRIBUIÇÃO AMOSTRAL DA MÉDIA </div><div class="t m0 x1 h5 y8 ff3 fs2 fc0 sc0 ls1a wsc">AMOSTRAL E TEOREMA CENTRAL DO </div><div class="t m0 x1 h5 y9 ff3 fs2 fc0 sc0 ls1a wsc">LIMITE </div><div class="t m0 x1 h6 ya ff3 fs3 fc1 sc0 ls1a wsc">Distribuição amostral da média amostral<span class="_0 blank"> </span> </div><div class="t m0 x1 h7 yb ff2 fs4 fc0 sc0 ls1a wsc">Seja <span class="ff4">\ue73a</span></div><div class="t m0 x3 h8 yc ff4 fs5 fc0 sc0 ls0">\ueb35<span class="fs4 ls1a ws0 v1">, \u2026 \ue73a</span></div><div class="t m0 x4 h9 yc ff4 fs5 fc0 sc0 ls1">\uebe1<span class="ff2 fs4 ls1a wsc v1"> a.a de tamanho <span class="ff4 ls2">\ue74a</span> de <span class="ff4 ls3">\ue73a</span>, com <span class="ff4 ls4">\ue727<span class="ls1a ws1 v2">[</span><span class="ls3">\ue73a<span class="ls5 v2">]</span><span class="ls1a ws2">= \ue7e4<span class="_0 blank"></span></span></span></span><span class="ls6"> e </span><span class="ff4 ws1">\ue738\ue73d\ue74e<span class="_0 blank"></span><span class="v2">(</span><span class="ls3">\ue73a<span class="ls5 v2">)</span></span><span class="ws3">=<span class="_1 blank"> </span>\ue7ea </span></span></span><span class="ls7 v3">\ueb36</span><span class="ff2 fs4 ls1a wsc v1">. Seja também </span></div><div class="t m0 x1 h7 yd ff4 fs4 fc0 sc0 ls1a">\ue73a</div><div class="t m0 x5 h7 ye ff4 fs4 fc0 sc0 ls8">\ued24<span class="ls9 v4">=</span><span class="fs5 ls1a v5">\ueb35</span></div><div class="t m0 x6 ha yf ff4 fs5 fc0 sc0 lsa">\uebe1<span class="fs4 lsb v6">\u2211<span class="ls1a v7">\ue73a</span></span></div><div class="t m0 x7 hb y10 ff4 fs5 fc0 sc0 ls1a">\uebdc</div><div class="t m0 x8 hb y11 ff4 fs5 fc0 sc0 ls1a">\uebe1</div><div class="t m0 x8 hb y12 ff4 fs5 fc0 sc0 ls1a ws4">\uebdc\ueb40\ueb35 <span class="ff2 fs4 wsc v8">. Então: </span></div><div class="t m0 x9 hc y13 ff5 fs4 fc0 sc0 ls1a ws5">\uf0b7<span class="ff6 lsc wsc"> <span class="ff4 ls4">\ue727<span class="ls1a ws1 v2">[</span><span class="ls1a">\ue73a</span></span></span></div><div class="t m0 xa h7 y14 ff4 fs4 fc0 sc0 lsd">\ued24<span class="ls5 v9">]</span><span class="ls1a ws2 v4">= \ue7e4<span class="_0 blank"></span><span class="ff2 wsc">. </span></span></div><div class="t m0 x9 hc y15 ff5 fs4 fc0 sc0 ls1a ws5">\uf0b7<span class="ff6 lsc wsc"> </span><span class="ff4 ws1">\ue738\ue73d\ue74e<span class="_0 blank"></span><span class="v2">(</span>\ue73a</span></div><div class="t m0 x7 h7 y16 ff4 fs4 fc0 sc0 lsd">\ued24<span class="ls5 v9">)</span><span class="lse v4">=</span><span class="fs5 lsf v5">\uec19</span><span class="fs6 ls1a va">\uec2e</span></div><div class="t m0 xb hb y17 ff4 fs5 fc0 sc0 ls10">\uebe1<span class="ff2 fs4 ls1a wsc vb"> </span></div><div class="t m0 x1 hd y18 ff2 fs4 fc1 sc0 ls1a wsc">População normal </div><div class="t m0 x1 h7 y19 ff2 fs4 fc0 sc0 ls1a wsc">Seja <span class="ff4">\ue73a</span></div><div class="t m0 x3 h8 y1a ff4 fs5 fc0 sc0 ls0">\ueb35<span class="fs4 ls1a ws0 v1">, \u2026 , \ue73a</span></div><div class="t m0 x7 h8 y1a ff4 fs5 fc0 sc0 ls11">\uebe1<span class="ff2 fs4 ls1a wsc v1"> a.a de <span class="ff4">\ue73a<span class="_1 blank"> </span>\u223c<span class="_1 blank"> </span>\ue730<span class="_0 blank"> </span>(\ue7e4<span class="_2 blank"> </span>,<span class="_3 blank"> </span> \ue7ea<span class="_2 blank"> </span></span></span><span class="ls7 v3">\ueb36</span><span class="fs4 ls1a ws1 v1">)<span class="ff2 wsc">. Então: </span></span></div><div class="t m0 xc h7 y1b ff4 fs4 fc0 sc0 ls1a">\ue73a</div><div class="t m0 xd he y1c ff4 fs4 fc0 sc0 ls8">\ued24<span class="ls1a wsc v4">\u223c<span class="_1 blank"> </span>\ue730<span class="_4 blank"> </span>\uf246\ue7e4<span class="_0 blank"></span>,<span class="_3 blank"> </span> <span class="_3 blank"> </span></span><span class="ls12 v6">\ue7ea</span><span class="fs5 ls1a vc">\ueb36</span></div><div class="t m0 xe hf y1d ff4 fs4 fc0 sc0 ls13">\ue74a<span class="ls6 va">\uf247<span class="ff2 ls1a wsc"> </span></span></div><div class="t m0 x1 hd y1e ff2 fs4 fc1 sc0 ls1a wsc">Amostra sem reposição </div><div class="t m0 x1 h7 y1f ff2 fs4 fc0 sc0 ls1a wsc">Seja <span class="ff4">\ue73a</span></div><div class="t m0 x3 h8 y20 ff4 fs5 fc0 sc0 ls0">\ueb35<span class="fs4 ls1a ws0 v1">, \u2026 , \ue73a</span></div><div class="t m0 x7 hb y20 ff4 fs5 fc0 sc0 ls11">\uebe1<span class="ff2 fs4 ls1a wsc v1"> amostra selecionada sem reposição de uma população fini<span class="_5 blank"></span>ta de </span></div><div class="t m0 x1 hc y21 ff2 fs4 fc0 sc0 ls1a wsc">tamanho <span class="ff4 ls14">\ue730</span>, com <span class="ff4 ls4">\ue727<span class="ls1a ws1 v2">[</span><span class="ls3">\ue73a<span class="ls5 v2">]</span><span class="ls1a ws2">= \ue7e4<span class="_0 blank"></span></span></span></span><span class="ls6"> e </span><span class="ff4 ws1">\ue738\ue73d\ue74e<span class="_0 blank"></span><span class="v2">(</span><span class="ls3">\ue73a<span class="ls5 v2">)</span></span><span class="ws3">=<span class="_1 blank"> </span>\ue7ea <span class="fs5 ls7 vd">\ueb36</span></span></span>. Considere <span class="ff4">\ue73a</span></div><div class="t m0 xf h7 y22 ff4 fs4 fc0 sc0 lsd">\ued24<span class="ff2 ls1a wsc v4"> a média amostral. Então: </span></div><div class="t m0 x9 hc y23 ff5 fs4 fc0 sc0 ls1a ws5">\uf0b7<span class="ff6 lsc wsc"> <span class="ff4 ls4">\ue727<span class="ls1a ws1 v2">[</span><span class="ls1a">\ue73a</span></span></span></div><div class="t m0 xa h7 y24 ff4 fs4 fc0 sc0 lsd">\ued24<span class="ls5 v9">]</span><span class="ls1a ws2 v4">= \ue7e4<span class="_0 blank"></span><span class="ff2 wsc">. </span></span></div><div class="t m0 x9 hc y25 ff5 fs4 fc0 sc0 ls1a ws5">\uf0b7<span class="ff6 lsc wsc"> </span><span class="ff4 ws1">\ue738\ue73d\ue74e<span class="_0 blank"></span><span class="v2">(</span>\ue73a</span></div><div class="t m0 x7 h7 y26 ff4 fs4 fc0 sc0 lsd">\ued24<span class="ls5 v9">)</span><span class="lse v4">=</span><span class="fs5 lsf v5">\uec19</span><span class="fs6 ls1a va">\uec2e</span></div><div class="t m0 xb h10 y27 ff4 fs5 fc0 sc0 ls15">\uebe1<span class="fs4 ls1a ws1 vb">\uf240</span><span class="ls1a ws6 ve">\uebc7\ueb3f\uebe1</span></div><div class="t m0 x10 h11 y27 ff4 fs5 fc0 sc0 ls1a ws7">\uebc7\ueb3f\ueb35 <span class="fs4 ws1 vb">\uf241<span class="ff2 wsc"> </span></span></div><div class="t m0 x1 hd y28 ff2 fs4 fc1 sc0 ls1a wsc">População normal </div><div class="t m0 x1 h7 y29 ff2 fs4 fc0 sc0 ls1a wsc">Seja <span class="ff4">\ue73a</span></div><div class="t m0 x3 h8 y2a ff4 fs5 fc0 sc0 ls0">\ueb35<span class="fs4 ls1a ws0 v1">, \u2026 , \ue73a</span></div><div class="t m0 x7 h12 y2a ff4 fs5 fc0 sc0 ls11">\uebe1<span class="ff2 fs4 ls1a wsc v1"> amostra selecionada sem reposição de uma população</span><span class="fs7 fc2 ls16 wsc v1"> </span><span class="fs4 ls1a ws8 v1">\ue73a \u223c</span></div><div class="t m0 x1 h13 y2b ff4 fs4 fc0 sc0 ls1a wsc">\ue730(\ue7e4,<span class="_6 blank"> </span> \ue7ea<span class="fs5 ls17 vf">2</span><span class="ws1">)</span><span class="ff2">, sendo </span><span class="ls3">\ue73a</span><span class="ff2"> população finita de tamanho </span><span class="ls14">\ue730</span><span class="ff2">. Então: </span></div><div class="t m0 x11 h7 y2c ff4 fs4 fc0 sc0 ls1a">\ue73a</div><div class="t m0 x12 he y2d ff4 fs4 fc0 sc0 ls18">\ued24<span class="ls1a ws9 v4">\u223c<span class="_1 blank"> </span>\ue730 </span><span class="ls6 v4">\ued6d</span><span class="ls1a wsc v4">\ue7e4,<span class="_4 blank"> </span> <span class="_3 blank"> </span></span><span class="ls12 v6">\ue7ea</span><span class="fs5 ls1a vc">\ueb36</span></div><div class="t m0 x13 h14 y2e ff4 fs4 fc0 sc0 ls19">\ue74a<span class="ls6 va">\ued6c</span><span class="ls1a wsa v10">\ue730<span class="_7 blank"> </span>\u2212 \ue74a</span></div><div class="t m0 x14 h15 y2e ff4 fs4 fc0 sc0 ls1a wsb">\ue730<span class="_7 blank"> </span>\u2212 1<span class="_0 blank"></span><span class="ws1 va">\ued70\ued71</span><span class="ff2 wsc va"> </span></div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/3c05a2a6-d21e-444d-ad65-e0025fe4005e/bg2.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1a wsc"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls1a wsc">2 </div><div class="c x1 y3 w2 h3"><div class="t m0 x0 h2 y4 ff1 fs0 fc0 sc0 ls1a wsc"> </div></div><div class="t m0 x1 hd y2f ff2 fs4 fc1 sc0 ls1a wsc">Variância populacional desconhecida </div><div class="t m0 x1 h7 y30 ff2 fs4 fc0 sc0 ls1a wsc">Nos casos em que <span class="ff4 ls12">\ue7ea<span class="fs5 ls7 vd">\ueb36</span></span> é desconhecida, então: </div><div class="t m0 x15 h7 y31 ff4 fs4 fc0 sc0 ls1a">\ue73a</div><div class="t m0 x16 h7 y32 ff4 fs4 fc0 sc0 ls1b">\ued24<span class="ls1a wsa v4">\u2212 \ue7e4</span></div><div class="t m0 x17 h7 y33 ff4 fs4 fc0 sc0 ls1a">\ue735</div><div class="t m0 x18 h16 y34 ff4 fs4 fc0 sc0 ls1a ws1">\u221a<span class="ls1c v11">\ue74a</span><span class="ws2 v12">\u223c \ue750</span><span class="fs5 ls1d v13">\uebe1</span><span class="ff2 wsc v12"> </span></div><div class="t m0 x1 h6 y35 ff3 fs3 fc1 sc0 ls1a wsc">Teorema Central do Limite (TCL) </div><div class="t m0 x1 h7 y36 ff2 fs4 fc0 sc0 ls1a wsc">Seja <span class="ff4 ls3">\ue73a</span> uma v.a com função de (densidade) de probabilid<span class="_5 blank"></span>ade <span class="ff4 wsd">\ue742 (\ue754 )</span>. Sejam <span class="ff4 ls1e">\ue7e4</span> e <span class="ff4 ls12">\ue7ea<span class="fs5 ls1f vd">\ueb36</span><span class="ls1a wse">< \u221e</span></span> a </div><div class="t m0 x1 h7 y37 ff2 fs4 fc0 sc0 ls1a wsc">média e variância de <span class="ff4 ls3">\ue73a</span>, respectivamente. </div><div class="t m0 x1 h7 y38 ff2 fs4 fc0 sc0 ls1a wsc">Seja <span class="ff4">\ue73a</span></div><div class="t m0 x19 h7 y39 ff4 fs4 fc0 sc0 lsd">\ued24<span class="ff2 ls1a wsc v4"> a média amostral de uma a.a de tamanho </span><span class="ls2 v4">\ue74a<span class="ff2 ls1a wsc"> de <span class="ff4 ls3">\ue73a</span>. Então, quando <span class="ff4 wsf">\ue74a \u2192 \u221e</span>, ou </span></span></div><div class="t m0 x1 hd y3a ff2 fs4 fc0 sc0 ls1a wsc">seja, n é suficientemente grande: </div><div class="t m0 x1a h7 y3b ff4 fs4 fc0 sc0 ls1a">\ue73a</div><div class="t m0 x1b h7 y3c ff4 fs4 fc0 sc0 ls1b">\ued24<span class="ls1a ws10 v4">\u2212<span class="_8 blank"> </span>\ue727 </span><span class="ls1a ws1 v9">[<span class="v7">\ue73a</span></span></div><div class="t m0 xd h7 y3c ff4 fs4 fc0 sc0 lsd">\ued24<span class="ls1a v9">]</span></div><div class="t m0 x1a h7 y3d ff4 fs4 fc0 sc0 ls20">\ueda5<span class="ls1a ws1 v7">\ue738\ue73d\ue74e<span class="_0 blank"></span><span class="v2">(</span>\ue73a</span></div><div class="t m0 xd h17 y3e ff4 fs4 fc0 sc0 lsd">\ued24<span class="ls5 v9">)</span><span class="ls21 v14">=</span><span class="ls1a v15">\ue73a</span></div><div class="t m0 x1c h7 y3c ff4 fs4 fc0 sc0 ls1b">\ued24<span class="ls1a wsa v4">\u2212 \ue7e4</span></div><div class="t m0 x1d h7 y3f ff4 fs4 fc0 sc0 ls1a">\ue7ea</div><div class="t m0 x13 h18 y40 ff4 fs4 fc0 sc0 ls1a ws1">\u221a<span class="ls1c v11">\ue74a</span><span class="ws11 v13">\u2248 \ue730<span class="_0 blank"></span>(0,1)<span class="ff2 wsc"> </span></span></div><div class="t m0 x1 hd y41 ff2 fs4 fc0 sc0 ls1a wsc"> </div><div class="t m0 x1 h19 y42 ff2 fs0 fc0 sc0 ls1a wsc"> </div><div class="t m0 x1 h19 y43 ff2 fs0 fc0 sc0 ls1a wsc"> </div></div><div class="pi" data-data='{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}'></div></div>