{"id":280,"date":"2023-08-03T04:08:56","date_gmt":"2023-08-03T04:08:56","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-de-variancia-amostral\/"},"modified":"2023-08-03T04:08:56","modified_gmt":"2023-08-03T04:08:56","slug":"distribuicao-de-variancia-amostral","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-de-variancia-amostral\/","title":{"rendered":"Distribui\u00e7\u00e3o amostral de vari\u00e2ncia"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 uma distribui\u00e7\u00e3o amostral de vari\u00e2ncia (ou distribui\u00e7\u00e3o amostral de vari\u00e2ncias) nas estat\u00edsticas. Da mesma forma, s\u00e3o apresentadas a f\u00f3rmula para a distribui\u00e7\u00e3o de vari\u00e2ncia amostral e um exerc\u00edcio resolvido passo a passo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-muestral-de-la-varianza\"><\/span> Qual \u00e9 a distribui\u00e7\u00e3o amostral de vari\u00e2ncia?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>distribui\u00e7\u00e3o amostral de vari\u00e2ncia<\/strong> \u00e9 a distribui\u00e7\u00e3o que resulta do c\u00e1lculo da vari\u00e2ncia de cada amostra poss\u00edvel de uma popula\u00e7\u00e3o. Ou seja, o conjunto de todas <a href=\"https:\/\/statorials.org\/pt\/desvio-amostral\/\">as vari\u00e2ncias amostrais<\/a> de todas as amostras poss\u00edveis de uma popula\u00e7\u00e3o forma a distribui\u00e7\u00e3o amostral de vari\u00e2ncia.<\/p>\n<p> Ou, em outras palavras, para obter a distribui\u00e7\u00e3o amostral da vari\u00e2ncia, devemos primeiro selecionar todas as amostras poss\u00edveis em uma popula\u00e7\u00e3o e depois calcular a vari\u00e2ncia de cada amostra selecionada. Assim, o conjunto de vari\u00e2ncias calculadas constitui a distribui\u00e7\u00e3o amostral da vari\u00e2ncia.<\/p>\n<p> Nas estat\u00edsticas, a distribui\u00e7\u00e3o amostral de vari\u00e2ncia \u00e9 usada para calcular a probabilidade de obter o valor da vari\u00e2ncia populacional extraindo uma \u00fanica amostra. Por exemplo, na an\u00e1lise de risco de investimento, \u00e9 utilizada a distribui\u00e7\u00e3o amostral de vari\u00e2ncia. <\/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-media\/\">Distribui\u00e7\u00e3o Amostral de M\u00e9dias<\/a><br \/> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/distribuicao-de-proporcao-amostral\/\">Distribui\u00e7\u00e3o amostral de propor\u00e7\u00f5es<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-muestral-de-la-varianza\"><\/span> F\u00f3rmula para distribui\u00e7\u00e3o amostral de vari\u00e2ncia<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A distribui\u00e7\u00e3o amostral de vari\u00e2ncia \u00e9 definida pela <a href=\"https:\/\/statorials.org\/pt\/distribuicao-qui-quadrado\/\">distribui\u00e7\u00e3o de probabilidade qui-quadrado<\/a> . 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<p> Esta f\u00f3rmula tamb\u00e9m \u00e9 usada para <a href=\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-variancia\/\">testar suposi\u00e7\u00f5es de vari\u00e2ncia<\/a> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-distribucion-muestral-de-la-varianza\"><\/span> Exemplo do mundo real da distribui\u00e7\u00e3o de vari\u00e2ncia amostral<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que vimos a defini\u00e7\u00e3o de distribui\u00e7\u00e3o amostral de vari\u00e2ncia e qual \u00e9 sua f\u00f3rmula, resolveremos um exemplo passo a passo para finalizar o entendimento do conceito.<\/p>\n<ul>\n<li> De uma popula\u00e7\u00e3o com vari\u00e2ncia conhecida \u03c3=5, \u00e9 escolhida uma amostra aleat\u00f3ria de 17 observa\u00e7\u00f5es. Qual \u00e9 a probabilidade de obter uma vari\u00e2ncia amostral maior que 10?<\/li>\n<\/ul>\n<p> Primeiro, precisamos obter a estat\u00edstica da distribui\u00e7\u00e3o de vari\u00e2ncia amostral. Portanto, aplicamos a f\u00f3rmula explicada na se\u00e7\u00e3o anterior:<\/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-fe66f077a5253dfe4d5b40d63fcec5ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2=\\cfrac{(n-1)s^2}{\\sigma^2}=\\cfrac{(17-1)\\cdot 10}{5}=32\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"274\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Como o tamanho da amostra \u00e9 n = 17, a distribui\u00e7\u00e3o qui-quadrado ter\u00e1 16 graus de liberdade (n-1). Portanto, a probabilidade da vari\u00e2ncia amostral ser superior a 10 equivale \u00e0 probabilidade de assumir um valor superior a 32 numa distribui\u00e7\u00e3o qui-quadrado com 16 graus de liberdade.<\/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-328d2cce8c284fc18c99a31b138bb113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[s^2>10]=P[\\chi_{16}^2>32]&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;20&#8243; width=&#8221;194&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p> Assim procuramos a probabilidade correspondente na tabela de distribui\u00e7\u00e3o qui-quadrado e assim resolvemos o problema.<\/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-ef8a9168b6d309653dc1f87ffbeace06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P[s^2>10]=P[\\chi_{16}^2>32]=0,01&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;20&#8243; width=&#8221;253&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p> Resumindo, a probabilidade de extrair uma amostra com vari\u00e2ncia superior a 10 \u00e9 de 1%.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 uma distribui\u00e7\u00e3o amostral de vari\u00e2ncia (ou distribui\u00e7\u00e3o amostral de vari\u00e2ncias) nas estat\u00edsticas. Da mesma forma, s\u00e3o apresentadas a f\u00f3rmula para a distribui\u00e7\u00e3o de vari\u00e2ncia amostral e um exerc\u00edcio resolvido passo a passo. Qual \u00e9 a distribui\u00e7\u00e3o amostral de vari\u00e2ncia? A distribui\u00e7\u00e3o amostral de vari\u00e2ncia \u00e9 a distribui\u00e7\u00e3o que resulta [&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-280","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>\u25b7 Distribui\u00e7\u00e3o amostral de vari\u00e2ncia<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o amostral de vari\u00e2ncia, sua f\u00f3rmula e um exemplo concreto de distribui\u00e7\u00e3o amostral de vari\u00e2ncia.\" \/>\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-variancia-amostral\/\" \/>\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 amostral de vari\u00e2ncia\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o amostral de vari\u00e2ncia, sua f\u00f3rmula e um exemplo concreto de distribui\u00e7\u00e3o amostral de vari\u00e2ncia.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/distribuicao-de-variancia-amostral\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T04:08:56+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3917636d4c911eeaad1a005195204d08_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=\"2 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-variancia-amostral\/\",\"url\":\"https:\/\/statorials.org\/pt\/distribuicao-de-variancia-amostral\/\",\"name\":\"\u25b7 Distribui\u00e7\u00e3o amostral de vari\u00e2ncia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T04:08:56+00:00\",\"dateModified\":\"2023-08-03T04:08:56+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a distribui\u00e7\u00e3o amostral de vari\u00e2ncia, sua f\u00f3rmula e um exemplo concreto de distribui\u00e7\u00e3o amostral de vari\u00e2ncia.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-de-variancia-amostral\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/distribuicao-de-variancia-amostral\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/distribuicao-de-variancia-amostral\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Distribui\u00e7\u00e3o amostral de vari\u00e2ncia\"}]},{\"@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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