{"id":286,"date":"2023-08-03T02:21:11","date_gmt":"2023-08-03T02:21:11","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-amostral-1\/"},"modified":"2023-08-03T02:21:11","modified_gmt":"2023-08-03T02:21:11","slug":"distribuicao-amostral-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-amostral-1\/","title":{"rendered":"Distribui\u00e7\u00e3o de amostras"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 distribui\u00e7\u00e3o amostral em estat\u00edsticas e para que ela \u00e9 usada. Assim voc\u00ea encontrar\u00e1 o significado de uma distribui\u00e7\u00e3o amostral, um exemplo concreto de distribui\u00e7\u00e3o amostral e, al\u00e9m disso, as f\u00f3rmulas para os tipos mais comuns de distribui\u00e7\u00f5es amostrais. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-muestral\"><\/span> Qual \u00e9 a distribui\u00e7\u00e3o amostral?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>distribui\u00e7\u00e3o amostral<\/strong> , ou <strong>distribui\u00e7\u00e3o amostral<\/strong> , \u00e9 a distribui\u00e7\u00e3o que resulta da considera\u00e7\u00e3o de todas as amostras poss\u00edveis de uma popula\u00e7\u00e3o. Em outras palavras, a distribui\u00e7\u00e3o amostral \u00e9 a distribui\u00e7\u00e3o obtida calculando um par\u00e2metro amostral de todas as amostras poss\u00edveis de uma popula\u00e7\u00e3o.<\/p>\n<p> Por exemplo, se extrairmos todas as amostras poss\u00edveis de uma popula\u00e7\u00e3o estat\u00edstica e calcularmos a m\u00e9dia de cada amostra, o conjunto de m\u00e9dias amostrais forma uma distribui\u00e7\u00e3o amostral. Mais precisamente, como o par\u00e2metro calculado \u00e9 a m\u00e9dia aritm\u00e9tica, \u00e9 a distribui\u00e7\u00e3o amostral da m\u00e9dia.<\/p>\n<p> Nas estat\u00edsticas, a distribui\u00e7\u00e3o amostral \u00e9 usada para calcular a probabilidade de aproxima\u00e7\u00e3o do valor do par\u00e2metro populacional ao estudar uma \u00fanica amostra. Da mesma forma, a distribui\u00e7\u00e3o amostral nos permite estimar o erro amostral para um determinado tamanho de amostra. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-distribucion-muestral\"><\/span> Exemplo de distribui\u00e7\u00e3o de amostragem<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que conhecemos a defini\u00e7\u00e3o de distribui\u00e7\u00e3o amostral, vejamos um exemplo simples para compreender totalmente o conceito.<\/p>\n<ul>\n<li> Numa caixa colocamos tr\u00eas bolas e cada uma tem um n\u00famero escrito de um a tr\u00eas, de forma que uma bola tem o n\u00famero 1, outra bola tem o n\u00famero 2 e a \u00faltima bola tem o n\u00famero 3. Para uma amostra de tamanho n = 2, calcula as probabilidades da distribui\u00e7\u00e3o amostral da m\u00e9dia se forem selecionadas amostras com reposi\u00e7\u00e3o.<\/li>\n<\/ul>\n<p> As amostras s\u00e3o selecionadas com reposi\u00e7\u00e3o, ou seja, a bola recolhida para selecionar o primeiro elemento da amostra \u00e9 devolvida \u00e0 caixa e pode ser selecionada novamente na segunda extra\u00e7\u00e3o. Portanto, todas as amostras poss\u00edveis da popula\u00e7\u00e3o s\u00e3o:<\/p>\n<p class=\"has-text-align-center\"> 1,1 1,2 1,3<br \/> 2,1 2,2 2,3<br \/> 3,1 3,2 3,3<\/p>\n<p> Assim, calculamos a m\u00e9dia aritm\u00e9tica de cada amostra poss\u00edvel: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-36b3a1e0bbb1be6eddc1a5d9899c5643_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{11}=\\cfrac{1+1}{2}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ff446066e6102f75d2d5435ad9dc46d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,2) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{12}=\\cfrac{1+2}{2}=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-904c1ee161fd7214c2c20ef15a038ea2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,3) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{13}=\\cfrac{1+3}{2}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4669b3b3d3ca07f035456cc50110134f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{21}=\\cfrac{2+1}{2}=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9fae1b39671fce31802b9ff66c8c1b9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2,2) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{22}=\\cfrac{2+2}{2}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fb036db8580a0d7389daddf6a938c541_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2,3) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{23}=\\cfrac{2+3}{2}=2,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7b77da5430a43732726cc62fb0fffe78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{31}=\\cfrac{3+1}{2}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5edbfa4f2b8752676ceba5ad0cd34d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,2) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{32}=\\cfrac{3+2}{2}=2,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bb60dfff5e3c5c090e019253ee84b198_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,3) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{33}=\\cfrac{3+3}{2}=3\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"296\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Portanto, as probabilidades de obter cada valor da m\u00e9dia amostral ao selecionar uma amostra aleat\u00f3ria da popula\u00e7\u00e3o s\u00e3o as seguintes: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/table-de-distribution-dechantillonnage.png\" alt=\"exemplo de tabela de distribui\u00e7\u00e3o de amostra\" class=\"wp-image-6145\" width=\"166\" height=\"195\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> As probabilidades da distribui\u00e7\u00e3o amostral apresentadas na tabela acima foram calculadas dividindo o n\u00famero de amostras com o referido valor m\u00e9dio pelo n\u00famero total de casos poss\u00edveis. Por exemplo: a m\u00e9dia amostral \u00e9 1,5 em dois casos entre nove poss\u00edveis, portanto P(1,5)=2\/9. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-distribuciones-muestrales\"><\/span> Tipos de distribui\u00e7\u00f5es amostrais<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> As distribui\u00e7\u00f5es amostrais (ou distribui\u00e7\u00f5es amostrais) podem ser classificadas com base no par\u00e2metro amostral a partir do qual foram obtidas. Portanto, os tipos mais comuns de distribui\u00e7\u00f5es s\u00e3o os seguintes:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Distribui\u00e7\u00e3o amostral da m\u00e9dia<\/strong> : \u00c9 a distribui\u00e7\u00e3o amostral que resulta do c\u00e1lculo da m\u00e9dia aritm\u00e9tica de cada amostra.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Distribui\u00e7\u00e3o Amostragem Proporcional<\/strong> : \u00c9 a distribui\u00e7\u00e3o amostral obtida calculando a propor\u00e7\u00e3o de todas as amostras.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Distribui\u00e7\u00e3o amostral de vari\u00e2ncia<\/strong> : Esta \u00e9 a distribui\u00e7\u00e3o amostral que forma o conjunto de todas as vari\u00e2ncias na amostra.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Distribui\u00e7\u00e3o amostral por diferen\u00e7a de m\u00e9dias<\/strong> : \u00e9 a distribui\u00e7\u00e3o amostral que resulta do c\u00e1lculo da diferen\u00e7a entre as m\u00e9dias de todas as amostras poss\u00edveis de duas popula\u00e7\u00f5es diferentes.<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Distribui\u00e7\u00e3o amostral por diferen\u00e7a de propor\u00e7\u00f5es<\/strong> : \u00e9 a distribui\u00e7\u00e3o amostral obtida subtraindo todas as propor\u00e7\u00f5es amostrais poss\u00edveis de duas popula\u00e7\u00f5es.<\/span><\/li>\n<\/ul>\n<p> Cada tipo de distribui\u00e7\u00e3o amostral \u00e9 explicado com mais detalhes abaixo. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-media\"><\/span> Distribui\u00e7\u00e3o amostral da m\u00e9dia<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Dada uma popula\u00e7\u00e3o que segue uma distribui\u00e7\u00e3o de probabilidade normal com m\u00e9dia<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> e desvio padr\u00e3o<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-eaaf379fee5e67946f3fedf5631047b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> e amostras de tamanho s\u00e3o extra\u00eddas<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> , a distribui\u00e7\u00e3o amostral da m\u00e9dia tamb\u00e9m ser\u00e1 definida por uma distribui\u00e7\u00e3o normal com as seguintes caracter\u00edsticas:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-44571aa7337b095ab9c9fa1f746e93a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\mu_{\\overline{x}}=\\mu \\qquad \\sigma_{\\overline{x}}=\\cfrac{\\sigma}{\\sqrt{n}}\\\\[4ex]\\displaystyle N_{\\overline{x}}\\left(\\mu, \\frac{\\sigma}{\\sqrt{n}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"159\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Ouro<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8ed084decbdfb365889aae767cf63e81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_{\\overline{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"20\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a m\u00e9dia da distribui\u00e7\u00e3o amostral da m\u00e9dia e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9067e28d896c7e5278763081c6cc40d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_{\\overline{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"19\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o seu desvio padr\u00e3o. Al\u00e9m disso,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7d78e2a2f2fae99a53eb087263cbb478_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\sigma}{\\sqrt{n}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"26\" style=\"vertical-align: -16px;\"><\/p>\n<p> \u00e9 o erro padr\u00e3o da distribui\u00e7\u00e3o amostral.<\/p>\n<p> <strong>Nota:<\/strong> Se a popula\u00e7\u00e3o n\u00e3o seguir uma distribui\u00e7\u00e3o normal, mas o tamanho da amostra for grande (n&gt;30), a distribui\u00e7\u00e3o amostral da m\u00e9dia tamb\u00e9m pode ser aproximada \u00e0 distribui\u00e7\u00e3o normal acima pelo limite do teorema central.<\/p>\n<p> Portanto, como a distribui\u00e7\u00e3o amostral da m\u00e9dia segue uma distribui\u00e7\u00e3o normal, a <strong>f\u00f3rmula para calcular qualquer probabilidade relacionada \u00e0 m\u00e9dia amostral<\/strong> \u00e9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ecd8bcb78b739c50d01b8bad563e5cb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\overline{x}-\\mu}{\\displaystyle\\frac{\\sigma}{\\sqrt{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"81\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a m\u00e9dia amostral.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> Esta \u00e9 a m\u00e9dia da popula\u00e7\u00e3o.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o desvio padr\u00e3o da popula\u00e7\u00e3o.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o tamanho da amostra.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 uma vari\u00e1vel definida pela distribui\u00e7\u00e3o normal padr\u00e3o N(0,1). <\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-amostral-da-media\/\">Exerc\u00edcio resolvido sobre distribui\u00e7\u00e3o amostral da m\u00e9dia<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-proporcion\"><\/span> Distribui\u00e7\u00e3o amostral de propor\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Na verdade, quando estudamos uma propor\u00e7\u00e3o de uma amostra, analisamos casos de sucesso. Portanto, a vari\u00e1vel aleat\u00f3ria em estudo segue uma distribui\u00e7\u00e3o de probabilidade binomial.<\/p>\n<p> De acordo com o teorema do limite central, para tamanhos grandes (n&gt;30) podemos aproximar uma distribui\u00e7\u00e3o binomial de uma distribui\u00e7\u00e3o normal. Portanto, <strong>a distribui\u00e7\u00e3o amostral da propor\u00e7\u00e3o se aproxima de uma distribui\u00e7\u00e3o normal com os seguintes par\u00e2metros:<\/strong><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f3408076893f390bb65baecfe38e6eff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle\\mu_{p}=p \\qquad \\sigma_{p}=\\sqrt{\\frac{pq}{n}}\\\\[4ex]\\displaystyle N_{p}\\left(p, \\sqrt{\\frac{pq}{n}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"168\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Ouro<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a probabilidade de sucesso e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-420eca7b6df080cc5f01773d1978f44a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a probabilidade de falha<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e1d214c21abe0d79fa453d635a025865_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q=1-p\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\"><\/p>\n<p> .<\/p>\n<p> <strong>Nota:<\/strong> Uma distribui\u00e7\u00e3o binomial s\u00f3 pode ser aproximada de uma distribui\u00e7\u00e3o normal se<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-88e275a965c091eb810599a07b0f8d46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n>30&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;52&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-41130f51ca4b83f1bf25b9dde90ecbfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"np\\ge 5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0af2ac5b6eb874f65b406b3bc39f0c7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"nq\\ge 5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<p> .<\/p>\n<p> Portanto, como a distribui\u00e7\u00e3o amostral da propor\u00e7\u00e3o pode ser aproximada a uma distribui\u00e7\u00e3o normal, a <strong>f\u00f3rmula para calcular qualquer probabilidade relacionada \u00e0 propor\u00e7\u00e3o de uma amostra<\/strong> \u00e9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5b7a4224240587268d0dd7865a33ac31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{pq}{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"78\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ecd29d136a62fc6b274e1181e064e20e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a propor\u00e7\u00e3o da amostra.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a propor\u00e7\u00e3o da popula\u00e7\u00e3o.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-420eca7b6df080cc5f01773d1978f44a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a probabilidade de falha da popula\u00e7\u00e3o,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e1d214c21abe0d79fa453d635a025865_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q=1-p\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\"><\/p>\n<p> .<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o tamanho da amostra.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 uma vari\u00e1vel definida pela distribui\u00e7\u00e3o normal padr\u00e3o N(0,1). <\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-de-proporcao-amostral\/\">Exerc\u00edcio resolvido sobre distribui\u00e7\u00e3o amostral da propor\u00e7\u00e3o<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-varianza\"><\/span> Distribui\u00e7\u00e3o amostral de vari\u00e2ncia<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A distribui\u00e7\u00e3o amostral de vari\u00e2ncia \u00e9 definida pela distribui\u00e7\u00e3o de probabilidade qui-quadrado. Portanto, a <strong>f\u00f3rmula para a estat\u00edstica da distribui\u00e7\u00e3o amostral de vari\u00e2ncia<\/strong> \u00e9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3917636d4c911eeaad1a005195204d08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2=\\cfrac{(n-1)s^2}{\\sigma^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"115\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-984dc78529fc235b078a9f3b62d0f0c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a estat\u00edstica da distribui\u00e7\u00e3o amostral de vari\u00e2ncia, que segue uma distribui\u00e7\u00e3o qui-quadrado.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o tamanho da amostra.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3ab572e85f9cb7cb6f495387f2a6ab0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a vari\u00e2ncia da amostra.<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c6d52162ef1ec2e8130fb00687aca707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a vari\u00e2ncia populacional. <\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-de-variancia-amostral\/\">Exerc\u00edcio resolvido sobre distribui\u00e7\u00e3o amostral de vari\u00e2ncia<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-diferencia-de-medias\"><\/span> Distribui\u00e7\u00e3o amostral de diferen\u00e7a de m\u00e9dias<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Se o tamanho da amostra for grande o suficiente (n <sub>1<\/sub> \u226530 en <sub>2<\/sub> \u226530), a distribui\u00e7\u00e3o amostral da diferen\u00e7a m\u00e9dia segue uma distribui\u00e7\u00e3o normal. Mais precisamente, os par\u00e2metros desta distribui\u00e7\u00e3o s\u00e3o calculados da seguinte forma:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-90c67b74b4e9326b7869d641a59725d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle \\mu_{\\overline{x_1}-\\overline{x_2}}=\\mu_1-\\mu_2 \\qquad \\sigma_{\\overline{x_1}-\\overline{x_2}}=\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}\\\\[6ex]\\displaystyle N_{\\overline{x_1}-\\overline{x_2}}\\left(\\mu_1-\\mu_2, \\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"328\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <strong>Nota:<\/strong> Se ambas as popula\u00e7\u00f5es forem distribui\u00e7\u00f5es normais, ent\u00e3o a distribui\u00e7\u00e3o amostral da diferen\u00e7a nas m\u00e9dias segue uma distribui\u00e7\u00e3o normal, independentemente do tamanho da amostra.<\/p>\n<p> Portanto, como a distribui\u00e7\u00e3o amostral da diferen\u00e7a de m\u00e9dias \u00e9 definida por uma distribui\u00e7\u00e3o normal, a <strong>f\u00f3rmula para calcular a estat\u00edstica da distribui\u00e7\u00e3o amostral da diferen\u00e7a<\/strong> de m\u00e9dias \u00e9:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-767964a3f07b303178ee08ec191eef43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{(\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"80\" width=\"203\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a4071a38558726a684ed069430c89fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 a m\u00e9dia da amostra i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-78e04dacbf6a47efcbdcc0417020dcbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a m\u00e9dia da popula\u00e7\u00e3o i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dc8c8f782c0ed8b7925012b60e174fa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o desvio padr\u00e3o da popula\u00e7\u00e3o i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o tamanho da amostra i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 uma vari\u00e1vel definida pela distribui\u00e7\u00e3o normal padr\u00e3o N(0,1).<\/li>\n<\/ul>\n<p> Observe que amostras de popula\u00e7\u00f5es diferentes podem ter tamanhos de amostra diferentes. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-amostral-da-diferenca-de-medias\/\">Exerc\u00edcio resolvido sobre distribui\u00e7\u00e3o amostral da diferen\u00e7a de m\u00e9dias<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-diferencia-de-proporciones\"><\/span> Distribui\u00e7\u00e3o amostral de diferen\u00e7a em propor\u00e7\u00f5es<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> As amostras selecionadas para a distribui\u00e7\u00e3o amostral por diferen\u00e7a de propor\u00e7\u00f5es s\u00e3o definidas por distribui\u00e7\u00f5es binomiais, porque para fins pr\u00e1ticos uma propor\u00e7\u00e3o \u00e9 uma raz\u00e3o entre casos de sucesso e o n\u00famero total de observa\u00e7\u00f5es.<\/p>\n<p> No entanto, devido ao teorema do limite central, as distribui\u00e7\u00f5es binomiais podem ser aproximadas \u00e0s distribui\u00e7\u00f5es normais de probabilidade. Portanto, a distribui\u00e7\u00e3o amostral da diferen\u00e7a de propor\u00e7\u00f5es pode ser aproximada a uma distribui\u00e7\u00e3o normal com as seguintes caracter\u00edsticas:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a1ce359b5dd6d80f8d27b0b9a1034bed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle\\mu_{\\widehat{p_1}-\\widehat{p_2}}=p_1-p_2 \\qquad \\sigma_{\\widehat{p_1}-\\widehat{p_2}}=\\sqrt{\\frac{p_1q_1}{n_1}+\\frac{p_2q_2}{n_2}}\\\\[6ex]\\displaystyle N_{p}\\left(p_1-p_2, \\sqrt{\\frac{p_1q_1}{n_1}+\\frac{p_2q_2}{n_2}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"122\" width=\"348\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> <strong>Nota:<\/strong> A distribui\u00e7\u00e3o amostral da diferen\u00e7a de propor\u00e7\u00f5es s\u00f3 pode ser aproximada de uma distribui\u00e7\u00e3o normal se<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6a7ebccb76a4ee9bbf44bb0f41ffee53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1\\geq30\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -3px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-93c3febf2679c77d41d7b319e262f298_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2\\geq 30\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -3px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-19a35b2095afa5133c32d92de163adaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1p_1\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"67\" style=\"vertical-align: -4px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a89c44bd89266e2fba37bf5211a6e30e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2p_2\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"67\" style=\"vertical-align: -4px;\"><\/p>\n<p> ,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-08c0b04a830a0062f4e7f25801c45fa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1q_1\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\"><\/p>\n<p> E<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-789e8bfde9b6a18c7ff9b1390feca142_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2q_2\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\"><\/p>\n<p> .<\/p>\n<p> Portanto, uma vez que a distribui\u00e7\u00e3o amostral da diferen\u00e7a de propor\u00e7\u00f5es pode ser aproximada de uma distribui\u00e7\u00e3o normal, a <strong>f\u00f3rmula para calcular a estat\u00edstica da distribui\u00e7\u00e3o amostral da diferen\u00e7a de propor\u00e7\u00f5es<\/strong> \u00e9 a seguinte:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a6b74dafd0599052a453e77646e5a77a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{(\\widehat{p_1}-\\widehat{p_2})-(p_1-p_2)}{\\displaystyle\\sqrt{\\frac{p_1q_1}{n_1}+\\frac{p_2q_2}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"198\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ad10d8ae9a51401d94ca9742249d6d15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a propor\u00e7\u00e3o da amostra i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a5db80b23c0dc6e4f21c509cb298856a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a propor\u00e7\u00e3o da popula\u00e7\u00e3o i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-4b2d0075b0f4fd8e4e14194b33ed0fe8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a probabilidade de falha da popula\u00e7\u00e3o i,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-917f2422b9b0d7d99ec3de548cc6bba3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q_i=1-p_i\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\"><\/p>\n<p> .<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o tamanho da amostra i.<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 uma vari\u00e1vel definida pela distribui\u00e7\u00e3o normal padr\u00e3o N(0,1). <\/li>\n<\/ul>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-amostral-da-diferenca-de-proporcoes\/\">Exerc\u00edcio resolvido sobre distribui\u00e7\u00e3o amostral da diferen\u00e7a de propor\u00e7\u00f5es<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 distribui\u00e7\u00e3o amostral em estat\u00edsticas e para que ela \u00e9 usada. Assim voc\u00ea encontrar\u00e1 o significado de uma distribui\u00e7\u00e3o amostral, um exemplo concreto de distribui\u00e7\u00e3o amostral e, al\u00e9m disso, as f\u00f3rmulas para os tipos mais comuns de distribui\u00e7\u00f5es amostrais. Qual \u00e9 a distribui\u00e7\u00e3o amostral? A distribui\u00e7\u00e3o amostral , ou distribui\u00e7\u00e3o [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-286","post","type-post","status-publish","format-standard","hentry","category-estatisticas"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>O que \u00e9 distribui\u00e7\u00e3o amostral? 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