{"id":246,"date":"2023-08-03T16:05:59","date_gmt":"2023-08-03T16:05:59","guid":{"rendered":"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-proporcao\/"},"modified":"2023-08-03T16:05:59","modified_gmt":"2023-08-03T16:05:59","slug":"intervalo-de-confianca-para-proporcao","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-proporcao\/","title":{"rendered":"Intervalo de confian\u00e7a para propor\u00e7\u00e3o"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 o intervalo de confian\u00e7a para propor\u00e7\u00e3o e para que ele \u00e9 usado nas estat\u00edsticas. Da mesma forma, voc\u00ea descobrir\u00e1 como calcular o intervalo de confian\u00e7a da propor\u00e7\u00e3o e tamb\u00e9m um exerc\u00edcio resolvido para melhor compreender o conceito. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-intervalo-de-confianza-para-la-proporcion\"><\/span> Qual \u00e9 o intervalo de confian\u00e7a da propor\u00e7\u00e3o?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O <strong>intervalo de confian\u00e7a para propor\u00e7\u00e3o<\/strong> \u00e9 um intervalo que fornece uma faixa de valores admiss\u00edveis para a propor\u00e7\u00e3o de uma popula\u00e7\u00e3o. Ou seja, o intervalo de confian\u00e7a da propor\u00e7\u00e3o indica um valor m\u00e1ximo e um valor m\u00ednimo entre os quais a propor\u00e7\u00e3o populacional se encontra com margem de erro.<\/p>\n<p> Por exemplo, se o intervalo de confian\u00e7a para a propor\u00e7\u00e3o de uma popula\u00e7\u00e3o com um n\u00edvel de confian\u00e7a de 95% for (0,73, 0,81), isso significa que a propor\u00e7\u00e3o de uma popula\u00e7\u00e3o est\u00e1 entre 73% e 81% com uma probabilidade de 95%.<\/p>\n<p> Portanto, o intervalo de confian\u00e7a da propor\u00e7\u00e3o \u00e9 utilizado para estimar o valor da propor\u00e7\u00e3o de uma popula\u00e7\u00e3o que atende a determinadas caracter\u00edsticas.<\/p>\n<p> Como veremos na pr\u00f3xima se\u00e7\u00e3o, o intervalo de confian\u00e7a para a propor\u00e7\u00e3o depende da propor\u00e7\u00e3o da amostra e do n\u00famero de observa\u00e7\u00f5es na amostra. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-intervalo-de-confianza-para-la-proporcion\"><\/span> F\u00f3rmula de intervalo de confian\u00e7a para propor\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O intervalo de confian\u00e7a para a propor\u00e7\u00e3o \u00e9 calculado somando e subtraindo da propor\u00e7\u00e3o amostral o valor de Z <sub>\u03b1\/2<\/sub> multiplicado pela raiz quadrada da propor\u00e7\u00e3o amostral (p) multiplicado por 1-p e dividido pelo tamanho da amostra (n). Portanto, a <strong>f\u00f3rmula para calcular o intervalo de confian\u00e7a da propor\u00e7\u00e3o<\/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-a328986eaa330c075c7fb85780df6411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(p-Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\ , \\ p+Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"339\" style=\"vertical-align: -23px;\"><\/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-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 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-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:7px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-6f8ee37ecf97c2a7c7d6dbe8fddddc27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_{\\alpha\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"34\" style=\"vertical-align: -8px;\"><\/p>\n<p> \u00e9 o quantil da distribui\u00e7\u00e3o normal padr\u00e3o correspondente a uma probabilidade de \u03b1\/2. Para amostras grandes e n\u00edvel de confian\u00e7a de 95% \u00e9 geralmente pr\u00f3ximo de 1,96 e para n\u00edvel de confian\u00e7a de 99% \u00e9 geralmente pr\u00f3ximo de 2,576. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-un-intervalo-de-confianza-para-la-proporcion\"><\/span> Exemplo de c\u00e1lculo de um intervalo de confian\u00e7a para propor\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para que voc\u00ea possa ver como \u00e9 calculado um intervalo de confian\u00e7a para a propor\u00e7\u00e3o, deixamos abaixo um exemplo concreto passo a passo.<\/p>\n<ul>\n<li> Uma seguradora deseja realizar uma pesquisa de mercado e determinar quantas pessoas em um pa\u00eds t\u00eam seguro de vida. Para isso, analisa-se uma amostra aleat\u00f3ria de 700 pessoas e chega-se \u00e0 conclus\u00e3o que 40% da amostra possui seguro de vida. Qual \u00e9 o intervalo de confian\u00e7a ao n\u00edvel de confian\u00e7a de 95% para a propor\u00e7\u00e3o da popula\u00e7\u00e3o do pa\u00eds?<\/li>\n<\/ul>\n<p> Para determinar o intervalo de confian\u00e7a da propor\u00e7\u00e3o populacional, precisamos usar a f\u00f3rmula que vimos acima:<\/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-a328986eaa330c075c7fb85780df6411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(p-Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\ , \\ p+Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"339\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p> Neste caso, queremos que o n\u00edvel de confian\u00e7a do intervalo de confian\u00e7a seja de 95%, ent\u00e3o o valor de Z <sub>\u03b1\/2<\/sub> que precisamos tomar \u00e9 1,96.<\/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-776a555edd1d064cf29a3a354caa5325_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1-\\alpha=0,95 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\alpha=0,05 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\alpha\/2=0,025\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"534\" style=\"vertical-align: -5px;\"><\/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-54dda39d0da5b29f2d25728b89565859_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}Z_{\\alpha\/2}= \\ \\color{orange}\\bm{?}\\\\[4ex]Z_{0,025}=1,96\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"71\" width=\"127\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> A declara\u00e7\u00e3o do problema j\u00e1 nos diz que o tamanho da amostra \u00e9 n=700 e a propor\u00e7\u00e3o observada na amostra \u00e9 p=0,40, ent\u00e3o substitu\u00edmos os dados na f\u00f3rmula do intervalo de confian\u00e7a para a propor\u00e7\u00e3o e calculamos os limites do intervalo: <\/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-a328986eaa330c075c7fb85780df6411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(p-Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\ , \\ p+Z_{\\alpha\/2}\\sqrt{\\frac{p(1-p)}{n}}\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"339\" style=\"vertical-align: -23px;\"><\/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-19482f8505723187c6106d6a1ab9ebb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(0,40-1,96\\cdot \\sqrt{\\frac{0,40\\cdot (1-0,40)}{700}}\\ , \\ 0,40+1,96\\cdot \\sqrt{\\frac{0,40\\cdot (1-0,40)}{700}\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"542\" style=\"vertical-align: -23px;\"><\/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-bc0b3de3cfa91d76192cb5cd5778aef6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(0,36 \\ , \\ 0,44\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Concluindo, a propor\u00e7\u00e3o da popula\u00e7\u00e3o estudada est\u00e1 entre 36% e 44% com um 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><br \/> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-variancia\/\">Intervalo de confian\u00e7a para vari\u00e2ncia<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 o intervalo de confian\u00e7a para propor\u00e7\u00e3o e para que ele \u00e9 usado nas estat\u00edsticas. Da mesma forma, voc\u00ea descobrir\u00e1 como calcular o intervalo de confian\u00e7a da propor\u00e7\u00e3o e tamb\u00e9m um exerc\u00edcio resolvido para melhor compreender o conceito. Qual \u00e9 o intervalo de confian\u00e7a da propor\u00e7\u00e3o? O intervalo de confian\u00e7a [&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-246","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 Intervalo de confian\u00e7a para propor\u00e7\u00e3o<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 qual \u00e9 o intervalo de confian\u00e7a da propor\u00e7\u00e3o, como ela \u00e9 calculada (f\u00f3rmula) e um exemplo concreto 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-proporcao\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Intervalo de confian\u00e7a para propor\u00e7\u00e3o\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 qual \u00e9 o intervalo de confian\u00e7a da propor\u00e7\u00e3o, como ela \u00e9 calculada (f\u00f3rmula) e um exemplo concreto passo a passo.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-proporcao\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T16:05:59+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a328986eaa330c075c7fb85780df6411_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\/intervalo-de-confianca-para-proporcao\/\",\"url\":\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-proporcao\/\",\"name\":\"\u25b7 Intervalo de confian\u00e7a para propor\u00e7\u00e3o\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T16:05:59+00:00\",\"dateModified\":\"2023-08-03T16:05:59+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 propor\u00e7\u00e3o, como ela \u00e9 calculada (f\u00f3rmula) e um exemplo concreto passo a passo.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-proporcao\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-proporcao\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-proporcao\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Intervalo de confian\u00e7a para propor\u00e7\u00e3o\"}]},{\"@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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