{"id":281,"date":"2023-08-03T03:50:30","date_gmt":"2023-08-03T03:50:30","guid":{"rendered":"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-a-diferenca-de-proporcoes\/"},"modified":"2023-08-03T03:50:30","modified_gmt":"2023-08-03T03:50:30","slug":"intervalo-de-confianca-para-a-diferenca-de-proporcoes","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/intervalo-de-confianca-para-a-diferenca-de-proporcoes\/","title":{"rendered":"Intervalo de confian\u00e7a para diferen\u00e7a de propor\u00e7\u00f5es"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 o intervalo de confian\u00e7a para a diferen\u00e7a de propor\u00e7\u00f5es nas estat\u00edsticas e para que ele \u00e9 usado. Voc\u00ea tamb\u00e9m descobrir\u00e1 como calcular o intervalo de confian\u00e7a para a diferen\u00e7a de duas propor\u00e7\u00f5es e um exerc\u00edcio resolvido 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-diferencia-de-proporciones\"><\/span> Qual \u00e9 o intervalo de confian\u00e7a para a diferen\u00e7a de propor\u00e7\u00f5es?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O <strong>intervalo de confian\u00e7a para diferen\u00e7a de propor\u00e7\u00f5es<\/strong> \u00e9 um intervalo que fornece uma faixa de valores aceit\u00e1veis entre os quais o valor da diferen\u00e7a entre as propor\u00e7\u00f5es de duas popula\u00e7\u00f5es se ajusta com um certo n\u00edvel de confian\u00e7a.<\/p>\n<p> Por exemplo, se o intervalo de confian\u00e7a para a diferen\u00e7a entre as propor\u00e7\u00f5es de duas popula\u00e7\u00f5es com um n\u00edvel de confian\u00e7a de 95% for (0,07, 15), isso significa que a diferen\u00e7a entre as duas propor\u00e7\u00f5es populacionais estar\u00e1 entre 7% e 15% com uma probabilidade de 95%.<\/p>\n<p> Portanto, nas estat\u00edsticas, o intervalo de confian\u00e7a para a diferen\u00e7a de propor\u00e7\u00f5es \u00e9 utilizado para estimar dois valores entre os quais liga a diferen\u00e7a entre duas propor\u00e7\u00f5es populacionais. S\u00e3o, portanto, coletadas duas amostras e a partir desses dados \u00e9 poss\u00edvel avaliar aproximadamente a diferen\u00e7a entre as propor\u00e7\u00f5es das popula\u00e7\u00f5es. <\/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-medias\/\">Intervalo de confian\u00e7a para diferen\u00e7a de m\u00e9dias<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-intervalo-de-confianza-para-la-diferencia-de-proporciones\"><\/span> F\u00f3rmula de intervalo de confian\u00e7a para diferen\u00e7a em propor\u00e7\u00f5es<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>f\u00f3rmula para calcular o intervalo de confian\u00e7a para a diferen\u00e7a de propor\u00e7\u00f5es<\/strong> com n\u00edvel de confian\u00e7a de 1-\u03b1 \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-73dd1f9d9a9245f9a3d48dbd29764cab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (\\widehat{p_1}-\\widehat{p_2})\\pm Z_{\\alpha\/2}\\sqrt{\\frac{\\widehat{p_1}(1-\\widehat{p_1})}{n_1}+\\frac{\\widehat{p_2}(1-\\widehat{p_2})}{n_2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"328\" 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-ad10d8ae9a51401d94ca9742249d6d15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a propor\u00e7\u00e3o da amostra i.<\/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-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.<\/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<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\/\">F\u00f3rmula de intervalo de confian\u00e7a para propor\u00e7\u00e3o<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-del-intervalo-de-confianza-para-la-diferencia-de-proporciones\"><\/span> Exemplo concreto de intervalo de confian\u00e7a para diferen\u00e7a de propor\u00e7\u00f5es<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de ver a defini\u00e7\u00e3o do intervalo de confian\u00e7a para a diferen\u00e7a de propor\u00e7\u00f5es e qual \u00e9 sua f\u00f3rmula, veremos um exemplo concreto de como \u00e9 calculado o intervalo de confian\u00e7a para a diferen\u00e7a de propor\u00e7\u00f5es.<\/p>\n<ul>\n<li> Queremos fazer um estudo estat\u00edstico sobre a propor\u00e7\u00e3o de canhotos, mais precisamente, queremos saber a diferen\u00e7a entre as propor\u00e7\u00f5es de canhotos entre homens e mulheres. Para isso, \u00e9 retirada uma amostra de 60 homens e uma amostra de 67 mulheres, entre as quais 5 homens e 7 mulheres s\u00e3o canhotos. Qual \u00e9 o intervalo de confian\u00e7a para a diferen\u00e7a de propor\u00e7\u00f5es com um n\u00edvel de confian\u00e7a de 95%?<\/li>\n<\/ul>\n<p> Primeiro, precisamos calcular a propor\u00e7\u00e3o de canhotos para cada amostra estat\u00edstica:<\/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-f71fe6b5e11cf7be2650ac723d4b69b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_1}=\\cfrac{5}{60}=0,083\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"128\" 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-43a2b255ab56c94be8d1227a1d532449_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_2}=\\cfrac{7}{67}=0,104\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"128\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Como vimos na se\u00e7\u00e3o acima, a f\u00f3rmula para determinar o intervalo de confian\u00e7a para a diferen\u00e7a de propor\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-73dd1f9d9a9245f9a3d48dbd29764cab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (\\widehat{p_1}-\\widehat{p_2})\\pm Z_{\\alpha\/2}\\sqrt{\\frac{\\widehat{p_1}(1-\\widehat{p_1})}{n_1}+\\frac{\\widehat{p_2}(1-\\widehat{p_2})}{n_2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"328\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> Assim, para encontrar o intervalo de confian\u00e7a para a diferen\u00e7a de propor\u00e7\u00f5es, precisamos determinar o valor de Z <sub>\u03b1<\/sub> \/2. Para fazer isso, usamos a <a href=\"https:\/\/statorials.org\/pt\/tabela-de-distribuicao-normal\/\">tabela de distribui\u00e7\u00e3o normal padr\u00e3o<\/a> .<\/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> Por fim, substitu\u00edmos os dados na f\u00f3rmula e calculamos o intervalo de confian\u00e7a para a diferen\u00e7a de propor\u00e7\u00f5es: <\/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-73dd1f9d9a9245f9a3d48dbd29764cab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (\\widehat{p_1}-\\widehat{p_2})\\pm Z_{\\alpha\/2}\\sqrt{\\frac{\\widehat{p_1}(1-\\widehat{p_1})}{n_1}+\\frac{\\widehat{p_2}(1-\\widehat{p_2})}{n_2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"328\" 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-697c9979fadd5a4a87952cdf3015109d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle (0,083-0,104)\\pm 1,96\\cdot \\sqrt{\\frac{0,083\\cdot(1-0,083)}{60}+\\frac{0,104\\cdot(1-0,104)}{67}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"526\" style=\"vertical-align: -13px;\"><\/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-0bb29f1bd8a63bf3114dd54c95fd7b53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle -0,021\\pm  0,101\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"121\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Resumindo, o intervalo de confian\u00e7a para a diferen\u00e7a nas propor\u00e7\u00f5es do problema \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-2b782f75c52b6dd00e8a46ea43b612e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-0,122 \\ , \\ 0,08)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" 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\/teste-de-hipotese-para-diferenca-em-proporcoes\/\">Teste de hip\u00f3teses para diferen\u00e7a em propor\u00e7\u00f5es<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 o intervalo de confian\u00e7a para a diferen\u00e7a de propor\u00e7\u00f5es nas estat\u00edsticas e para que ele \u00e9 usado. Voc\u00ea tamb\u00e9m descobrir\u00e1 como calcular o intervalo de confian\u00e7a para a diferen\u00e7a de duas propor\u00e7\u00f5es e um exerc\u00edcio resolvido passo a passo. Qual \u00e9 o intervalo de confian\u00e7a para a diferen\u00e7a de [&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-281","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>Intervalo de confian\u00e7a para diferen\u00e7a de propor\u00e7\u00f5es<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 qual \u00e9 o intervalo de confian\u00e7a para a diferen\u00e7a de propor\u00e7\u00f5es, como ele \u00e9 calculado (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\" 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