{"id":242,"date":"2023-08-03T17:24:22","date_gmt":"2023-08-03T17:24:22","guid":{"rendered":"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-variancia\/"},"modified":"2023-08-03T17:24:22","modified_gmt":"2023-08-03T17:24:22","slug":"intervalo-de-confianca-para-variancia","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-variancia\/","title":{"rendered":"Intervalo de confian\u00e7a para vari\u00e2ncia"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 o intervalo de confian\u00e7a para vari\u00e2ncia e para que ele \u00e9 usado nas estat\u00edsticas. Da mesma forma, voc\u00ea aprender\u00e1 como calcular o intervalo de confian\u00e7a da vari\u00e2ncia e um exerc\u00edcio passo a passo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-intervalo-de-confianza-para-la-varianza\"><\/span> Qual \u00e9 o intervalo de confian\u00e7a para a vari\u00e2ncia?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O <strong>intervalo de confian\u00e7a para vari\u00e2ncia<\/strong> \u00e9 um intervalo que aproxima os valores entre os quais se encontra a vari\u00e2ncia de uma popula\u00e7\u00e3o. Ou seja, o intervalo de confian\u00e7a da vari\u00e2ncia indica o valor m\u00e1ximo e o valor m\u00ednimo da vari\u00e2ncia populacional para um n\u00edvel de confian\u00e7a.<\/p>\n<p> Por exemplo, se o intervalo de confian\u00e7a de 95% para uma vari\u00e2ncia populacional for (55,75), isso significa que a vari\u00e2ncia populacional estar\u00e1 entre 55 e 75 com 95% de probabilidade.<\/p>\n<p> Portanto, o intervalo de confian\u00e7a da vari\u00e2ncia \u00e9 usado para estimar dois valores entre os quais se encontra a vari\u00e2ncia populacional. A vari\u00e2ncia amostral pode ser calculada, mas a vari\u00e2ncia populacional geralmente \u00e9 desconhecida, portanto o intervalo de confian\u00e7a da vari\u00e2ncia nos permite aproximar seu valor. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-intervalo-de-confianza-para-la-varianza\"><\/span> F\u00f3rmula de intervalo de confian\u00e7a para vari\u00e2ncia<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para calcular o intervalo de confian\u00e7a para a vari\u00e2ncia de uma popula\u00e7\u00e3o, \u00e9 utilizada a <a href=\"https:\/\/statorials.org\/pt\/distribuicao-qui-quadrado\/\">distribui\u00e7\u00e3o qui-quadrado<\/a> . Mais especificamente, a <strong>f\u00f3rmula para calcular o intervalo de confian\u00e7a da 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-c81b971afee9691573e8400dc0945c37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( (n-1)\\frac{s^2}{\\chi_{n-1;\\alpha\/2}} \\ , \\ (n-1)\\frac{s^2}{\\chi_{n-1;1-\\alpha\/2}}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"304\" style=\"vertical-align: -20px;\"><\/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-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-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 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-a1f2f5b5bd065f40d0b8c175d6d48950_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{n-1;\\alpha\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"64\" style=\"vertical-align: -8px;\"><\/p>\n<p> \u00e9 o valor da distribui\u00e7\u00e3o qui-quadrado com n-1 graus de liberdade para uma probabilidade menor que \u03b1\/2.<\/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-f1726e9973441084f7ac98c5550f1b23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{n-1;1-\\alpha\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -8px;\"><\/p>\n<p> \u00e9 o valor da distribui\u00e7\u00e3o Qui-quadrado com n-1 graus de liberdade para uma probabilidade superior a 1-\u03b1\/2. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-del-intervalo-de-confianza-para-la-varianza\"><\/span> Exemplo de c\u00e1lculo do intervalo de confian\u00e7a para vari\u00e2ncia<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para que voc\u00ea possa entender melhor o conceito, nesta se\u00e7\u00e3o deixamos um exemplo resolvido de como \u00e9 calculado o intervalo de confian\u00e7a para a vari\u00e2ncia.<\/p>\n<ul>\n<li> Temos uma amostra de 8 observa\u00e7\u00f5es com os valores mostrados abaixo. Qual \u00e9 o intervalo de confian\u00e7a para a vari\u00e2ncia populacional com um n\u00edvel de confian\u00e7a de 1-\u03b1=95%?<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"> 206 203 201 212<br \/> 194 176 208 201<\/p>\n<p> Conforme explicado acima, a f\u00f3rmula para determinar o intervalo de confian\u00e7a da vari\u00e2ncia populacional \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-c81b971afee9691573e8400dc0945c37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( (n-1)\\frac{s^2}{\\chi_{n-1;\\alpha\/2}} \\ , \\ (n-1)\\frac{s^2}{\\chi_{n-1;1-\\alpha\/2}}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"304\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> Portanto, para encontrar o intervalo de confian\u00e7a, devemos primeiro calcular o desvio padr\u00e3o amostral: <\/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-0710aa65b2fb918489f96dbe762b9478_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s=11,13\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"76\" style=\"vertical-align: -4px;\"><\/p>\n<\/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\/desvio-padrao-ou-desvio-padrao\/\">Como calcular o desvio padr\u00e3o<\/a><\/div>\n<p> Em segundo lugar, olhamos para a tabela de distribui\u00e7\u00e3o qui-quadrado para ver quais s\u00e3o os valores correspondentes que precisamos: <\/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-b68ae2b68b8c4caabf162f13aa199c5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\chi_{n-1;\\alpha\/2}= \\ \\color{orange}\\bm{?}\\\\[2ex]\\chi_{_{7;0,025}}=16,013\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"156\" style=\"vertical-align: 0px;\"><\/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-07baae9e30db85030d566f59b660a7f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\chi_{n-1;1-\\alpha\/2}= \\ \\color{orange}\\bm{?}\\\\[2ex]\\chi_{_{7;0,975}}=1,690\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"56\" width=\"174\" style=\"vertical-align: 0px;\"><\/p>\n<\/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> Valores da tabela de distribui\u00e7\u00e3o qui-quadrado<\/div>\n<p> Ent\u00e3o inserimos os valores na f\u00f3rmula do intervalo de confian\u00e7a para a vari\u00e2ncia e fazemos o c\u00e1lculo: <\/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-c81b971afee9691573e8400dc0945c37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( (n-1)\\frac{s^2}{\\chi_{n-1;\\alpha\/2}} \\ , \\ (n-1)\\frac{s^2}{\\chi_{n-1;1-\\alpha\/2}}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"47\" width=\"304\" style=\"vertical-align: -20px;\"><\/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-d9c72782ebf40d0fb3d0f63bd052c68b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( (8-1)\\frac{11,13^2}{16,013} \\ , \\ (8-1)\\frac{11,13^2}{1,690}\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"257\" style=\"vertical-align: -17px;\"><\/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-6878d54e28345cc23afa271c4441948a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left( 54,15 \\ , \\ 513,10\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"127\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Concluindo, a vari\u00e2ncia da popula\u00e7\u00e3o estudada est\u00e1 entre 54,15 e 513,10 com n\u00edvel de confian\u00e7a de 95%. <\/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\/intervalo-de-confianca-para-a-media\/\">Intervalo de confian\u00e7a para a m\u00e9dia<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 o intervalo de confian\u00e7a para vari\u00e2ncia e para que ele \u00e9 usado nas estat\u00edsticas. Da mesma forma, voc\u00ea aprender\u00e1 como calcular o intervalo de confian\u00e7a da vari\u00e2ncia e um exerc\u00edcio passo a passo. Qual \u00e9 o intervalo de confian\u00e7a para a vari\u00e2ncia? O intervalo de confian\u00e7a para vari\u00e2ncia \u00e9 [&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-242","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>\u25b7Intervalo de confian\u00e7a para varia\u00e7\u00e3o<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 qual \u00e9 o intervalo de confian\u00e7a da vari\u00e2ncia, como ele \u00e9 calculado (f\u00f3rmula) e um exerc\u00edcio resolvido passo a passo.\" \/>\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\/intervalo-de-confianca-para-variancia\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7Intervalo de confian\u00e7a para varia\u00e7\u00e3o\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 qual \u00e9 o intervalo de confian\u00e7a da vari\u00e2ncia, como ele \u00e9 calculado (f\u00f3rmula) e um exerc\u00edcio resolvido passo a passo.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-variancia\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T17:24:22+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c81b971afee9691573e8400dc0945c37_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\/intervalo-de-confianca-para-variancia\/\",\"url\":\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-variancia\/\",\"name\":\"\u25b7Intervalo de confian\u00e7a para varia\u00e7\u00e3o\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T17:24:22+00:00\",\"dateModified\":\"2023-08-03T17:24:22+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 qual \u00e9 o intervalo de confian\u00e7a da vari\u00e2ncia, como ele \u00e9 calculado (f\u00f3rmula) e um exerc\u00edcio resolvido passo a passo.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-variancia\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-variancia\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-variancia\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Intervalo de confian\u00e7a para 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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