{"id":284,"date":"2023-08-03T03:02:31","date_gmt":"2023-08-03T03:02:31","guid":{"rendered":"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-diferenca-em-proporcoes\/"},"modified":"2023-08-03T03:02:31","modified_gmt":"2023-08-03T03:02:31","slug":"teste-de-hipotese-para-diferenca-em-proporcoes","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-diferenca-em-proporcoes\/","title":{"rendered":"Teste de hip\u00f3teses para diferen\u00e7a em propor\u00e7\u00f5es"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 teste de hip\u00f3tese para diferen\u00e7a de propor\u00e7\u00f5es. Voc\u00ea tamb\u00e9m aprender\u00e1 como realizar um teste de hip\u00f3tese sobre a diferen\u00e7a de propor\u00e7\u00f5es, bem como um exerc\u00edcio passo a passo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-prueba-de-hipotesis-para-la-diferencia-de-proporciones\"><\/span> Qual \u00e9 o teste de hip\u00f3tese para a diferen\u00e7a de propor\u00e7\u00f5es?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>O teste de hip\u00f3tese de diferen\u00e7a de propor\u00e7\u00e3o<\/strong> \u00e9 um m\u00e9todo usado para rejeitar ou aceitar a hip\u00f3tese de que as propor\u00e7\u00f5es de duas popula\u00e7\u00f5es s\u00e3o diferentes. Ou seja, o teste de hip\u00f3tese de diferen\u00e7a de propor\u00e7\u00e3o \u00e9 usado para determinar se duas propor\u00e7\u00f5es populacionais s\u00e3o iguais ou n\u00e3o.<\/p>\n<p> Tenha em mente que as decis\u00f5es tomadas em testes de hip\u00f3teses s\u00e3o baseadas em um n\u00edvel de confian\u00e7a previamente estabelecido, portanto n\u00e3o se pode garantir que o resultado de um teste de hip\u00f3teses esteja sempre correto, mas sim que este \u00e9 o resultado mais prov\u00e1vel que seja verdadeiro. <\/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\/um-nivel-de-confianca\/\">Qual \u00e9 o n\u00edvel de confian\u00e7a? (Estatisticas)<\/a><\/div>\n<p> O teste de hip\u00f3teses para a diferen\u00e7a de duas propor\u00e7\u00f5es envolve calcular a estat\u00edstica de teste e compar\u00e1-la com o valor cr\u00edtico para rejeitar ou n\u00e3o a hip\u00f3tese nula. A seguir explicaremos detalhadamente como realizar um teste de hip\u00f3tese sobre a diferen\u00e7a de propor\u00e7\u00f5es.<\/p>\n<p> Finalmente, lembre-se de que, em estat\u00edstica, o teste de hip\u00f3teses tamb\u00e9m pode ser chamado de contraste de hip\u00f3teses, teste de hip\u00f3tese ou teste de signific\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\/teste-de-hipotese-para-a-diferenca-de-medias\/\">Teste de hip\u00f3teses para a diferen\u00e7a de m\u00e9dias<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-prueba-de-hipotesis-para-la-diferencia-de-proporciones\"><\/span> F\u00f3rmula de teste de hip\u00f3teses para diferen\u00e7a em propor\u00e7\u00f5es<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>f\u00f3rmula para calcular a estat\u00edstica do teste de hip\u00f3tese para a diferen\u00e7a nas propor\u00e7\u00f5es<\/strong> de duas popula\u00e7\u00f5es \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-161267e1562535b8ded23017389e0807_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\displaystyle (\\widehat{p_1}-\\widehat{p_2})-(p_1-p_2)}{\\displaystyle \\sqrt{p_0(1-p_0)\\left(\\frac{1}{n_1}+\\frac{1}{n_2}\\right)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"229\" style=\"vertical-align: -52px;\"><\/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-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a estat\u00edstica de teste de hip\u00f3tese para a diferen\u00e7a de propor\u00e7\u00f5es.<\/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-023bcfb3fa329ff4f481163d36b65bf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a propor\u00e7\u00e3o da popula\u00e7\u00e3o 1.<\/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-1a0ac2d00900c29ac35c13956874c642_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a propor\u00e7\u00e3o da popula\u00e7\u00e3o 2.<\/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-a4c76b176c372799a3a3a7aa8858eecf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a propor\u00e7\u00e3o da amostra 1.<\/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-cd7916af5298a603fad64ab8fb2501a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a propor\u00e7\u00e3o da amostra 2.<\/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-cebc0a013985f2695aeb53ded9e7afb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o tamanho da amostra 1.<\/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-bf1e42c248eee22a0911c24c95fe28f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o tamanho da amostra 2.<\/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-ccd892ed2f60029f47331cf785d30482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a propor\u00e7\u00e3o combinada das duas amostras.<\/li>\n<\/ul>\n<p> A propor\u00e7\u00e3o combinada das duas amostras \u00e9 calculada da seguinte forma:<\/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-6f349422474d622468a6a14f445f2eb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_0=\\cfrac{x_1+x_2}{n_1+n_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"102\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> Ouro<\/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-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o n\u00famero de resultados na amostra iy<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o tamanho da amostra i. <\/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-diferenca-de-proporcoes\/\">Intervalo de confian\u00e7a para diferen\u00e7a de propor\u00e7\u00f5es<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-prueba-de-hipotesis-para-la-diferencia-de-proporciones\"><\/span> Exemplo concreto de teste de hip\u00f3tese para diferen\u00e7a de propor\u00e7\u00f5es<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para terminar de ver o que envolve o teste de hip\u00f3tese para a diferen\u00e7a de propor\u00e7\u00f5es, um exemplo resolvido passo a passo desse tipo de teste de hip\u00f3tese \u00e9 mostrado abaixo.<\/p>\n<ul>\n<li> Queremos analisar se existe diferen\u00e7a significativa no efeito de dois medicamentos usados para a mesma doen\u00e7a. Para isso, um dos medicamentos \u00e9 aplicado em uma amostra de 60 pacientes e 48 pessoas ficam curadas. Por outro lado, o outro medicamento \u00e9 aplicado em uma amostra de 65 pacientes e 55 est\u00e3o curados. Realize um teste de hip\u00f3tese com n\u00edvel de signific\u00e2ncia de 5% para determinar se a porcentagem de pessoas curadas por cada medicamento \u00e9 diferente.<\/li>\n<\/ul>\n<p> A hip\u00f3tese de teste para este problema consiste nas seguintes hip\u00f3teses nulas e hip\u00f3teses alternativas:<\/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-06d3762df12e74f2c5204a5e57f4e451_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: p_1-p_2=0\\\\[2ex] H_1:p_1-p_2\\neq 0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"137\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Primeiro, calculamos a propor\u00e7\u00e3o de cada amostra dividindo o n\u00famero de casos de sucesso pelo tamanho da amostra:<\/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-cb931a4f209ae3f6468f761d9a1978c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_1}=\\cfrac{48}{60}=0,80\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"119\" style=\"vertical-align: -12px;\"><\/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-3946308ea76348e30ec338f8500ee655_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_1}=\\cfrac{55}{65}=0,85\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"118\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Encontramos ent\u00e3o a propor\u00e7\u00e3o combinada das duas amostras:<\/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-e536a515c55598373f535a15de012c5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_0=\\cfrac{48+55}{60+65}=0,82\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"158\" style=\"vertical-align: -14px;\"><\/p>\n<\/p>\n<p> A seguir, aplicamos a f\u00f3rmula de teste de hip\u00f3tese para a diferen\u00e7a de propor\u00e7\u00f5es para calcular a estat\u00edstica de teste:<\/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-a9f3f8f1a427577abac02e3f6c119be8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle Z&amp;=\\frac{\\displaystyle (\\widehat{p_1}-\\widehat{p_2})-(p_1-p_2)}{\\displaystyle \\sqrt{p_0(1-p_0)\\left(\\frac{1}{n_1}+\\frac{1}{n_2}\\right)}}\\\\[2ex]\\displaystyle Z&amp;=\\frac{\\displaystyle (0,80-0,85)-0}{\\displaystyle \\sqrt{0,82\\cdot(1-0,82)\\left(\\frac{1}{60}+\\frac{1}{65}\\right)}}\\\\[2ex]\\displaystyle Z&amp;=-0,73 \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"218\" width=\"277\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Em contraste, procuramos o valor cr\u00edtico do teste de hip\u00f3tese na <a href=\"https:\/\/statorials.org\/pt\/tabela-de-distribuicao-normal\/\">Tabela Z.<\/a> Como o n\u00edvel de signific\u00e2ncia \u00e9 0,05 e este \u00e9 um teste de hip\u00f3tese bicaudal, o valor cr\u00edtico do teste \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-8154fa6e5bfee35698c6dc26928cd98c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha=0,05 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\alpha\/2=0,025\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"300\" 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> Tal que o valor absoluto da estat\u00edstica do teste seja menor que o valor cr\u00edtico, portanto, a hip\u00f3tese alternativa \u00e9 rejeitada e a hip\u00f3tese nula do teste \u00e9 aceita. <\/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-f336118d0fd06640ec390f85b90d1086_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|-0,73|=0,73<1,96 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Se rechaza } H_1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"423\" style=\"vertical-align: -5px;\"><\/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\/distribuicao-amostral-da-diferenca-de-proporcoes\/\">Distribui\u00e7\u00e3o Amostragem de Diferen\u00e7a em Propor\u00e7\u00f5es<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 teste de hip\u00f3tese para diferen\u00e7a de propor\u00e7\u00f5es. Voc\u00ea tamb\u00e9m aprender\u00e1 como realizar um teste de hip\u00f3tese sobre a diferen\u00e7a de propor\u00e7\u00f5es, bem como um exerc\u00edcio passo a passo. Qual \u00e9 o teste de hip\u00f3tese para a diferen\u00e7a de propor\u00e7\u00f5es? O teste de hip\u00f3tese de diferen\u00e7a de propor\u00e7\u00e3o \u00e9 um [&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-284","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 Teste de hip\u00f3tese para diferen\u00e7a de propor\u00e7\u00f5es<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 o teste de hip\u00f3tese para diferen\u00e7a de propor\u00e7\u00f5es, como ele \u00e9 realizado (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\/teste-de-hipotese-para-diferenca-em-proporcoes\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Teste de hip\u00f3tese para diferen\u00e7a de propor\u00e7\u00f5es\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 o teste de hip\u00f3tese para diferen\u00e7a de propor\u00e7\u00f5es, como ele \u00e9 realizado (f\u00f3rmula) e um exemplo concreto.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-diferenca-em-proporcoes\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T03:02:31+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-161267e1562535b8ded23017389e0807_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\/teste-de-hipotese-para-diferenca-em-proporcoes\/\",\"url\":\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-diferenca-em-proporcoes\/\",\"name\":\"\u25b7 Teste de hip\u00f3tese para diferen\u00e7a de propor\u00e7\u00f5es\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T03:02:31+00:00\",\"dateModified\":\"2023-08-03T03:02:31+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 o teste de hip\u00f3tese para diferen\u00e7a de propor\u00e7\u00f5es, como ele \u00e9 realizado (f\u00f3rmula) e um exemplo concreto.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-diferenca-em-proporcoes\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-diferenca-em-proporcoes\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-diferenca-em-proporcoes\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Teste de hip\u00f3teses para diferen\u00e7a em propor\u00e7\u00f5es\"}]},{\"@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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