{"id":218,"date":"2023-08-04T01:16:05","date_gmt":"2023-08-04T01:16:05","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-de-alunos\/"},"modified":"2023-08-04T01:16:05","modified_gmt":"2023-08-04T01:16:05","slug":"distribuicao-de-alunos","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-de-alunos\/","title":{"rendered":"Distribui\u00e7\u00e3o t de estudante"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o t de Student e para que ela \u00e9 usada. Al\u00e9m disso, \u00e9 mostrado o gr\u00e1fico da distribui\u00e7\u00e3o t de Student e quais s\u00e3o as caracter\u00edsticas desse tipo de distribui\u00e7\u00e3o de probabilidade. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-t-de-student\"><\/span> Qual \u00e9 a distribui\u00e7\u00e3o do aluno?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>distribui\u00e7\u00e3o t de Student<\/strong> \u00e9 uma distribui\u00e7\u00e3o de probabilidade amplamente utilizada em estat\u00edstica. Especificamente, a distribui\u00e7\u00e3o t de Student \u00e9 utilizada no teste t de Student para determinar a diferen\u00e7a entre as m\u00e9dias de duas amostras e para estabelecer intervalos de confian\u00e7a.<\/p>\n<p> A distribui\u00e7\u00e3o t de Student foi desenvolvida pelo estat\u00edstico William Sealy Gosset em 1908 sob o pseud\u00f4nimo de &#8220;Student&#8221;.<\/p>\n<p> A distribui\u00e7\u00e3o t de Student \u00e9 definida pelo seu n\u00famero de graus de liberdade, obtido subtraindo uma unidade do n\u00famero total de observa\u00e7\u00f5es. Portanto, a f\u00f3rmula para determinar os graus de liberdade de uma distribui\u00e7\u00e3o t de Student \u00e9 <em>\u03bd=n-1<\/em> . <\/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-1c805dc2d6ca050feb70dad99de53402_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\nu=n-1\\\\[2ex]X\\sim t_\\nu\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"74\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"grafica-de-la-distribucion-t-de-student\"><\/span> Gr\u00e1fico de distribui\u00e7\u00e3o t de Student<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que conhecemos a defini\u00e7\u00e3o da distribui\u00e7\u00e3o t de Student, vamos ver qual \u00e9 o seu gr\u00e1fico. Assim, a seguir voc\u00ea pode ver graficamente v\u00e1rios exemplos de distribui\u00e7\u00f5es t de Student com diferentes graus de liberdade. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/graphique-de-distribution-t-des-etudiants.png\" alt=\"Gr\u00e1fico de distribui\u00e7\u00e3o t de Student\" class=\"wp-image-4266\" width=\"700\" height=\"420\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> A partir do gr\u00e1fico da distribui\u00e7\u00e3o t de Student, as seguintes propriedades podem ser deduzidas:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">A distribui\u00e7\u00e3o t de Student \u00e9 sim\u00e9trica centrada em 0 e tem formato de sino.<\/span><\/li>\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">A distribui\u00e7\u00e3o t de Student \u00e9 mais dispersa que a distribui\u00e7\u00e3o normal, ou seja, a curva da distribui\u00e7\u00e3o t de Student \u00e9 mais larga.<\/span><\/li>\n<li style=\"margin-bottom:14px\"> <span style=\"color:#101010;font-weight: normal;\">Quanto mais graus de liberdade a distribui\u00e7\u00e3o t de Student tiver, menor ser\u00e1 sua dispers\u00e3o.<\/span><\/li>\n<\/ul>\n<p> No gr\u00e1fico acima, a fun\u00e7\u00e3o densidade da distribui\u00e7\u00e3o t de Student foi plotada em rela\u00e7\u00e3o aos seus graus de liberdade. No entanto, voc\u00ea pode ver abaixo como a fun\u00e7\u00e3o de probabilidade cumulativa da distribui\u00e7\u00e3o t de Student varia: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-t-etudiante-cumulative.png\" alt=\"gr\u00e1fico da distribui\u00e7\u00e3o t cumulativa de Student\" class=\"wp-image-4267\" width=\"700\" height=\"420\" srcset=\"\" sizes=\"auto, \"><\/figure>\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\/tabela-de-distribuicao-t-do-aluno\/\">Tabela de distribui\u00e7\u00e3o dos alunos<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-t-de-student\"><\/span> Caracter\u00edsticas da distribui\u00e7\u00e3o t de Student<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> As caracter\u00edsticas mais importantes da distribui\u00e7\u00e3o t de Student s\u00e3o mostradas abaixo.<\/p>\n<ul>\n<li> O dom\u00ednio da distribui\u00e7\u00e3o t de Student consiste em n\u00fameros reais.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-fd8ca9914bdf447012a1a16f7950ce95_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\\in (-\\infty, +\\infty)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"116\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Para distribui\u00e7\u00f5es t de Student com mais de um grau de liberdade, a m\u00e9dia da distribui\u00e7\u00e3o \u00e9 igual a 0.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-d4fed5eadcaa1162752aeedb7f8a0906_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim t_\\nu\\\\[2ex] E[X]=0 \\qquad \\text{para }\\nu>1\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;55&#8243; width=&#8221;190&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> A vari\u00e2ncia de uma distribui\u00e7\u00e3o t de Student pode ser calculada usando a seguinte express\u00e3o:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bfdcbc8a5f071a61e091b0ef6f686a16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim t_\\nu\\\\[2ex] Var(X)=\\cfrac{\\nu}{\\nu-2} \\qquad \\text{para }\\nu>2\\end{array} &#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;75&#8243; width=&#8221;245&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> A mediana e a moda da distribui\u00e7\u00e3o t de Student, independentemente do n\u00famero de graus de liberdade, s\u00e3o sempre 0.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8d90790fce0c987648c0b30216c82214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Me=0\\\\[2ex]Mo=0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"60\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> A fun\u00e7\u00e3o densidade da distribui\u00e7\u00e3o t de Student \u00e9 definida pela seguinte f\u00f3rmula:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-8c0f1e97a8e407e8b9e2b00ba93aee0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]=\\frac{\\Gamma((\\nu+1)\/2)} {\\sqrt{\\nu\\pi}\\,\\Gamma(\\nu\/2)} (1+x^2\/\\nu)^{-(\\nu+1)\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"339\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> A fun\u00e7\u00e3o de distribui\u00e7\u00e3o de probabilidade cumulativa da distribui\u00e7\u00e3o t de Student \u00e9 definida pela seguinte f\u00f3rmula:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-da1e3bdf2d87c3a7dcc89c236958dcec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\frac{1}{2} + x \\Gamma \\left( \\frac{\\nu+1}{2} \\right) \\cdot\\frac{\\,_2F_1 \\left ( \\frac{1}{2},\\frac{\\nu+1}{2};\\frac{3}{2};-\\frac{x^2}{\\nu} \\right)}{\\sqrt{\\pi\\nu}\\,\\Gamma \\left(\\frac{\\nu}{2}\\right)}\" title=\"Rendered by QuickLaTeX.com\" height=\"59\" width=\"402\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<ul>\n<li> Para distribui\u00e7\u00f5es t de Student com graus de liberdade superiores a 3, o coeficiente de assimetria \u00e9 zero porque \u00e9 uma distribui\u00e7\u00e3o sim\u00e9trica.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6fea0ec5e37ef4db61fb44d6f5eba6fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=0\\qquad \\text{para }\\nu>3&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;17&#8243; width=&#8221;164&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<\/p>\n<ul>\n<li> Se os graus de liberdade da distribui\u00e7\u00e3o t de Student forem superiores a quatro, a curtose pode ser calculada dividindo seis pelos graus de liberdade menos quatro. <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0335e705ad289732dd1be59dc8388dee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle C=\\cfrac{6}{\\nu-4}\\qquad \\text{para }\\nu>4&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;38&#8243; width=&#8221;198&#8243; style=&#8221;vertical-align: -12px;&#8221;><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"aplicaciones-de-la-distribucion-t-de-student\"><\/span> Aplica\u00e7\u00f5es da distribui\u00e7\u00e3o t de Student<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A distribui\u00e7\u00e3o t de Student \u00e9 uma distribui\u00e7\u00e3o de probabilidade amplamente utilizada em estat\u00edstica. Na verdade, existe at\u00e9 o teste t de Student, que \u00e9 utilizado para testar hip\u00f3teses e intervalos de confian\u00e7a.<\/p>\n<p> Assim, a distribui\u00e7\u00e3o t de Student permite analisar a diferen\u00e7a entre as m\u00e9dias de duas amostras, mais precisamente, \u00e9 utilizada para determinar se duas amostras possuem m\u00e9dias significativamente diferentes. Da mesma forma, o teste t de Student \u00e9 utilizado para saber se a reta obtida a partir de uma an\u00e1lise de regress\u00e3o linear tem inclina\u00e7\u00e3o ou n\u00e3o.<\/p>\n<p> Em suma, as aplica\u00e7\u00f5es da distribui\u00e7\u00e3o t de Student baseiam-se na an\u00e1lise de conjuntos de dados que teoricamente seguem uma distribui\u00e7\u00e3o normal, mas o n\u00famero total de observa\u00e7\u00f5es \u00e9 demasiado pequeno para utilizar este tipo de distribui\u00e7\u00e3o.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o t de Student e para que ela \u00e9 usada. Al\u00e9m disso, \u00e9 mostrado o gr\u00e1fico da distribui\u00e7\u00e3o t de Student e quais s\u00e3o as caracter\u00edsticas desse tipo de distribui\u00e7\u00e3o de probabilidade. Qual \u00e9 a distribui\u00e7\u00e3o do aluno? A distribui\u00e7\u00e3o t de Student \u00e9 uma distribui\u00e7\u00e3o de probabilidade [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"class_list":["post-218","post","type-post","status-publish","format-standard","hentry","category-probabilidade"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Distribui\u00e7\u00e3o dos alunos<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o t de Student, para que serve, o gr\u00e1fico da distribui\u00e7\u00e3o t de Student e suas caracter\u00edsticas.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pt\/distribuicao-de-alunos\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Distribui\u00e7\u00e3o dos alunos\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o t de Student, para que serve, o gr\u00e1fico da distribui\u00e7\u00e3o t de Student e suas caracter\u00edsticas.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-de-alunos\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-04T01:16:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1c805dc2d6ca050feb70dad99de53402_l3.png\" \/>\n<meta name=\"author\" content=\"Dr. benjamim anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. benjamim anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo estimado de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-de-alunos\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-de-alunos\/\",\"name\":\"\u25b7 Distribui\u00e7\u00e3o dos alunos\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-04T01:16:05+00:00\",\"dateModified\":\"2023-08-04T01:16:05+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o t de Student, para que serve, o gr\u00e1fico da distribui\u00e7\u00e3o t de Student e suas caracter\u00edsticas.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-de-alunos\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-de-alunos\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-de-alunos\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribui\u00e7\u00e3o t de estudante\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pt\/#website\",\"url\":\"https:\/\/statorials.org\/pt\/\",\"name\":\"Statorials\",\"description\":\"O seu guia para a literacia estat\u00edstica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-PT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\",\"name\":\"Dr. benjamim anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-PT\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. benjamim anderson\"},\"description\":\"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. 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