{"id":268,"date":"2023-08-03T08:29:13","date_gmt":"2023-08-03T08:29:13","guid":{"rendered":"https:\/\/statorials.org\/pt\/proporcao-da-amostra\/"},"modified":"2023-08-03T08:29:13","modified_gmt":"2023-08-03T08:29:13","slug":"proporcao-da-amostra","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/proporcao-da-amostra\/","title":{"rendered":"Propor\u00e7\u00e3o da amostra"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 propor\u00e7\u00e3o de amostra em estat\u00edsticas. Assim, voc\u00ea descobrir\u00e1 como calcular a propor\u00e7\u00e3o amostral, um exerc\u00edcio resolvido e, tamb\u00e9m, qual a diferen\u00e7a entre a propor\u00e7\u00e3o amostral e a propor\u00e7\u00e3o populacional. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-proporcion-muestral\"><\/span> Qual \u00e9 a propor\u00e7\u00e3o da amostra?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A propor\u00e7\u00e3o da amostra<\/strong> \u00e9 a propor\u00e7\u00e3o de casos de sucesso em uma amostra em rela\u00e7\u00e3o ao tamanho da amostra. Portanto, para calcular a propor\u00e7\u00e3o da amostra, o n\u00famero de sucessos na amostra deve ser dividido pelo n\u00famero total de dados.<\/p>\n<p> O s\u00edmbolo para propor\u00e7\u00e3o da amostra \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-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> .<\/p>\n<p> Nas estat\u00edsticas, quando se realiza um inqu\u00e9rito, normalmente nem todos os dados populacionais s\u00e3o conhecidos, raz\u00e3o pela qual normalmente se realiza um estudo de uma amostra representativa e depois as conclus\u00f5es tiradas s\u00e3o extrapoladas para toda a popula\u00e7\u00e3o. popula\u00e7\u00e3o. Assim, a propor\u00e7\u00e3o da amostra \u00e9 usada para estimar a propor\u00e7\u00e3o de toda a popula\u00e7\u00e3o. Abaixo veremos como isso \u00e9 feito. <\/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\/amostra-representativa-1\/\">O que s\u00e3o amostras representativas?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-proporcion-muestral\"><\/span> Exemplo de f\u00f3rmula de propor\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A propor\u00e7\u00e3o da amostra \u00e9 igual ao n\u00famero de casos de sucesso na amostra dividido pelo tamanho da amostra. Portanto, a <strong>f\u00f3rmula para c\u00e1lculo da propor\u00e7\u00e3o 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-8497d73f09738f45701a70350badaacd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}=\\cfrac{e}{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"46\" 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 style=\"margin-bottom:3px\">\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:3px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-558a73dc6903ad0c33580b0ce9f110d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o n\u00famero de casos de sucesso na amostra.<\/li>\n<li style=\"margin-bottom:3px\">\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 n\u00famero total de itens de dados na amostra. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-la-proporcion-muestral\"><\/span> Exemplo de c\u00e1lculo de propor\u00e7\u00e3o de amostra<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de ver a defini\u00e7\u00e3o de propor\u00e7\u00e3o amostral e qual \u00e9 sua f\u00f3rmula, nesta se\u00e7\u00e3o resolveremos um exemplo simples para que voc\u00ea possa ver como a propor\u00e7\u00e3o amostral \u00e9 calculada.<\/p>\n<ul>\n<li> Uma empresa fabrica um brinquedo e compra uma de suas pe\u00e7as de outra empresa externa. Por\u00e9m, dentro dos lotes que compra aparecem pe\u00e7as defeituosas, por isso ele decide fazer um estudo estat\u00edstico para saber a propor\u00e7\u00e3o de pe\u00e7as em bom estado e a propor\u00e7\u00e3o de defeitos. Ent\u00e3o, voc\u00ea pede uma amostra de 1.000 unidades e encontra 138 pe\u00e7as defeituosas. Qual \u00e9 a propor\u00e7\u00e3o de pe\u00e7as em bom estado na amostra? E qual \u00e9 a propor\u00e7\u00e3o de pe\u00e7as defeituosas na amostra?<\/li>\n<\/ul>\n<p> O n\u00famero de pe\u00e7as n\u00e3o danificadas na amostra \u00e9 1.000 menos o n\u00famero de pe\u00e7as defeituosas:<\/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-eba1cfb3b37e9124aa6a8f3d61ba3023_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e=1000-138=862\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"165\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Ent\u00e3o, para encontrar a propor\u00e7\u00e3o amostral, aplicamos 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-becf48230461723d7a4d320217ad95fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}=\\cfrac{e}{n}=\\cfrac{862}{1000}=0,862\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"174\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> A propor\u00e7\u00e3o da amostra de pe\u00e7as em bom estado \u00e9, portanto, de 86,2%.<\/p>\n<p> Por outro lado, a propor\u00e7\u00e3o de pe\u00e7as defeituosas equivale a um menos a propor\u00e7\u00e3o de pe\u00e7as boas:<\/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-14b45b7c5bc9fb8770efa40fac1f9e45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{q}=1-\\widehat{p}=1-0,862=0,138\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"237\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> A propor\u00e7\u00e3o amostral de pe\u00e7as defeituosas \u00e9, portanto, de 13,8%. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"proporcion-muestral-y-proporcion-poblacional\"><\/span> Propor\u00e7\u00e3o da amostra e propor\u00e7\u00e3o da popula\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>propor\u00e7\u00e3o da popula\u00e7\u00e3o<\/strong> \u00e9 a propor\u00e7\u00e3o da popula\u00e7\u00e3o estat\u00edstica. Ou seja, a propor\u00e7\u00e3o populacional \u00e9 a rela\u00e7\u00e3o dos casos de sucesso de uma popula\u00e7\u00e3o estudada em rela\u00e7\u00e3o a todos os elementos que fazem parte dessa popula\u00e7\u00e3o.<\/p>\n<p> Portanto, a <strong>diferen\u00e7a entre a propor\u00e7\u00e3o nacional e a propor\u00e7\u00e3o populacional<\/strong> \u00e9 que a propor\u00e7\u00e3o nacional \u00e9 a propor\u00e7\u00e3o dos casos de maioria, em mudan\u00e7a, a propor\u00e7\u00e3o populacional refere-se \u00e0 propor\u00e7\u00e3o de casos de eventos respeitando todos os elementos Popula\u00e7\u00e3o.<\/p>\n<p> Para diferenciar a propor\u00e7\u00e3o amostral da propor\u00e7\u00e3o populacional, elas s\u00e3o representadas por s\u00edmbolos diferentes. O s\u00edmbolo para propor\u00e7\u00e3o da amostra \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-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> , enquanto o s\u00edmbolo da propor\u00e7\u00e3o da popula\u00e7\u00e3o \u00e9<\/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> .<\/p>\n<p> Em geral, a propor\u00e7\u00e3o populacional n\u00e3o pode ser determinada com precis\u00e3o, porque nem todos os valores populacionais s\u00e3o normalmente conhecidos. Em vez disso, o valor da propor\u00e7\u00e3o da popula\u00e7\u00e3o \u00e9 geralmente estimado utilizando um intervalo de confian\u00e7a com a seguinte f\u00f3rmula:<\/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-6517d510181870c58b167c4d9712a7a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\widehat{p}-Z_{\\alpha\/2}\\sqrt{\\frac{\\widehat{p}(1-\\widehat{p})}{n}}\\ , \\ \\widehat{p}+Z_{\\alpha\/2}\\sqrt{\\frac{\\widehat{p}(1-\\widehat{p})}{n}}\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"339\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p> Para ver como a propor\u00e7\u00e3o da popula\u00e7\u00e3o \u00e9 estimada, clique no seguinte link: <\/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-proporcao\/\">Intervalo de confian\u00e7a para propor\u00e7\u00e3o populacional<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-proporciones\"><\/span> Distribui\u00e7\u00e3o amostral de propor\u00e7\u00f5es<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Por fim, veremos em que consiste uma distribui\u00e7\u00e3o amostral de propor\u00e7\u00f5es, pois \u00e9 um conceito estat\u00edstico relacionado \u00e0 propor\u00e7\u00e3o amostral.<\/p>\n<p> Primeiro, vamos come\u00e7ar definindo o que \u00e9 uma distribui\u00e7\u00e3o amostral. Uma <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 estat\u00edstica.<\/p>\n<p> Portanto, uma <strong>distribui\u00e7\u00e3o amostral de propor\u00e7\u00f5es<\/strong> \u00e9 a distribui\u00e7\u00e3o que resulta do c\u00e1lculo da propor\u00e7\u00e3o de cada amostra poss\u00edvel de uma popula\u00e7\u00e3o. Ou seja, se estudarmos todas as amostras poss\u00edveis de uma popula\u00e7\u00e3o e calcularmos a propor\u00e7\u00e3o de cada uma das amostras, o conjunto de valores calculado \u00e9 uma distribui\u00e7\u00e3o amostral de propor\u00e7\u00f5es amostrais.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 propor\u00e7\u00e3o de amostra em estat\u00edsticas. Assim, voc\u00ea descobrir\u00e1 como calcular a propor\u00e7\u00e3o amostral, um exerc\u00edcio resolvido e, tamb\u00e9m, qual a diferen\u00e7a entre a propor\u00e7\u00e3o amostral e a propor\u00e7\u00e3o populacional. Qual \u00e9 a propor\u00e7\u00e3o da amostra? A propor\u00e7\u00e3o da amostra \u00e9 a propor\u00e7\u00e3o de casos de sucesso em uma amostra [&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-268","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>\u25b7Propor\u00e7\u00e3o da amostra<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a propor\u00e7\u00e3o da amostra nas estat\u00edsticas, como a propor\u00e7\u00e3o da amostra \u00e9 calculada (f\u00f3rmula) e um exemplo concreto.\" \/>\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\/proporcao-da-amostra\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7Propor\u00e7\u00e3o da amostra\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a propor\u00e7\u00e3o da amostra nas estat\u00edsticas, como a propor\u00e7\u00e3o da amostra \u00e9 calculada (f\u00f3rmula) e um exemplo concreto.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/proporcao-da-amostra\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T08:29:13+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ecd29d136a62fc6b274e1181e064e20e_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=\"4 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/proporcao-da-amostra\/\",\"url\":\"https:\/\/statorials.org\/pt\/proporcao-da-amostra\/\",\"name\":\"\u25b7Propor\u00e7\u00e3o da amostra\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T08:29:13+00:00\",\"dateModified\":\"2023-08-03T08:29:13+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 a propor\u00e7\u00e3o da amostra nas estat\u00edsticas, como a propor\u00e7\u00e3o da amostra \u00e9 calculada (f\u00f3rmula) e um exemplo concreto.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/proporcao-da-amostra\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/proporcao-da-amostra\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/proporcao-da-amostra\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Propor\u00e7\u00e3o da amostra\"}]},{\"@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. Com vasta experi\u00eancia e conhecimento na \u00e1rea de estat\u00edstica, estou empenhado em compartilhar meu conhecimento para capacitar os alunos por meio de Statorials. 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