{"id":260,"date":"2023-08-03T11:07:43","date_gmt":"2023-08-03T11:07:43","guid":{"rendered":"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-proporcao\/"},"modified":"2023-08-03T11:07:43","modified_gmt":"2023-08-03T11:07:43","slug":"teste-de-hipotese-para-proporcao","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-proporcao\/","title":{"rendered":"Teste de hip\u00f3tese para propor\u00e7\u00e3o"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 o teste de hip\u00f3tese de propor\u00e7\u00e3o nas estat\u00edsticas. Voc\u00ea encontrar\u00e1, portanto, a f\u00f3rmula do teste de hip\u00f3tese da propor\u00e7\u00e3o e, al\u00e9m disso, um exerc\u00edcio passo a passo para entender perfeitamente como isso \u00e9 feito. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-prueba-de-hipotesis-para-la-proporcion\"><\/span> O que \u00e9 teste de hip\u00f3tese para propor\u00e7\u00e3o?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>O teste de hip\u00f3tese de propor\u00e7\u00e3o<\/strong> \u00e9 um m\u00e9todo estat\u00edstico usado para determinar se deve ou n\u00e3o rejeitar a hip\u00f3tese nula de uma propor\u00e7\u00e3o populacional.<\/p>\n<p> Assim, dependendo do valor da estat\u00edstica do teste de hip\u00f3tese para a propor\u00e7\u00e3o e o n\u00edvel de signific\u00e2ncia, a hip\u00f3tese nula \u00e9 rejeitada ou aceita.<\/p>\n<p> Observe que o teste de hip\u00f3tese tamb\u00e9m pode ser chamado de contraste de hip\u00f3tese, teste de hip\u00f3tese ou teste de signific\u00e2ncia. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-prueba-de-hipotesis-para-la-proporcion\"><\/span> F\u00f3rmula de teste de hip\u00f3teses para propor\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A estat\u00edstica do teste de hip\u00f3tese para a propor\u00e7\u00e3o \u00e9 igual \u00e0 diferen\u00e7a na propor\u00e7\u00e3o da amostra menos o valor proposto da propor\u00e7\u00e3o dividido pelo desvio padr\u00e3o da propor\u00e7\u00e3o.<\/p>\n<p> A <strong>f\u00f3rmula da hip\u00f3tese de teste para a propor\u00e7\u00e3o<\/strong> \u00e9, portanto:<\/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-e2f5ad36dae72cd89279809ab3ea6d20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{p(1-p)}{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"67\" width=\"123\" style=\"vertical-align: -41px;\"><\/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 do teste de hip\u00f3tese para a propor\u00e7\u00e3o.<\/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-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>\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 o valor da propor\u00e7\u00e3o proposta.<\/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-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>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-661a2bbf8dccd197bcf450330420cbc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\sqrt{\\frac{p(1-p)}{n}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"84\" style=\"vertical-align: -13px;\"><\/p>\n<p> \u00e9 o desvio padr\u00e3o da propor\u00e7\u00e3o.<\/li>\n<\/ul>\n<p> Tenha em mente que n\u00e3o basta calcular a estat\u00edstica do teste de hip\u00f3tese para a propor\u00e7\u00e3o, mas o resultado deve ent\u00e3o ser interpretado:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a propor\u00e7\u00e3o for bilateral, a hip\u00f3tese nula \u00e9 rejeitada se o valor absoluto da estat\u00edstica for maior que o valor cr\u00edtico Z <sub>\u03b1\/2<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a propor\u00e7\u00e3o corresponder \u00e0 cauda direita, a hip\u00f3tese nula \u00e9 rejeitada se a estat\u00edstica for maior que o valor cr\u00edtico Z <sub>\u03b1<\/sub> .<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Se o teste de hip\u00f3tese para a propor\u00e7\u00e3o corresponder \u00e0 cauda esquerda, a hip\u00f3tese nula \u00e9 rejeitada se a estat\u00edstica for menor que o valor cr\u00edtico -Z <sub>\u03b1<\/sub> .<\/span><\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7d5bd583532769e3014286e8ffd94c9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: p\\neq p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |Z|>Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: p> p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: p< p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z<-Z_{\\alpha} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"437\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Lembre-se de que os valores cr\u00edticos podem ser facilmente obtidos na tabela de distribui\u00e7\u00e3o normal. <\/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\/tabela-de-distribuicao-normal\/\">Tabela de distribui\u00e7\u00e3o normal<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-prueba-de-hipotesis-para-la-proporcion\"><\/span> Exemplo de teste de hip\u00f3teses para propor\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Assim que vermos a defini\u00e7\u00e3o de teste de hip\u00f3tese para propor\u00e7\u00e3o e qual \u00e9 sua f\u00f3rmula, resolveremos um exemplo para entender melhor o conceito.<\/p>\n<ul>\n<li> Segundo o fabricante, um medicamento contra uma doen\u00e7a espec\u00edfica tem 70% de efic\u00e1cia. Em laborat\u00f3rio testamos a efic\u00e1cia desse medicamento, pois os pesquisadores acreditam que a propor\u00e7\u00e3o \u00e9 diferente. Para isso, o medicamento \u00e9 testado em uma amostra de 1.000 pacientes e 641 pessoas s\u00e3o curadas. Realizar um teste de hip\u00f3tese sobre a propor\u00e7\u00e3o populacional com n\u00edvel de signific\u00e2ncia de 5% para rejeitar ou n\u00e3o a hip\u00f3tese dos pesquisadores.<\/li>\n<\/ul>\n<p> Neste caso, <a href=\"https:\/\/statorials.org\/pt\/hipotese-nula-e-alternativa\/\">a hip\u00f3tese nula e a hip\u00f3tese alternativa<\/a> do teste de hip\u00f3tese para a propor\u00e7\u00e3o populacional s\u00e3o:<\/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-f7da8281eeecc022e2ec7daea6a9756e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: p=0,70\\\\[2ex] H_1:p\\neq 0,70 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"117\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> A propor\u00e7\u00e3o de pessoas na amostra que foram curadas pelo medicamento \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-93865dbb1097265b35967f0138a51d89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}=\\cfrac{641}{1000}=0,641\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"137\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Calculamos a estat\u00edstica do teste de hip\u00f3tese para a propor\u00e7\u00e3o aplicando a f\u00f3rmula vista 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-e689388b0a73e91c1e3d8812c2c4c42a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\displaystyle Z&amp;=\\frac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{p(1-p)}{n}}}\\\\[2ex]Z&amp;=\\frac{0,641-0,70}{\\displaystyle\\sqrt{\\frac{0,70\\cdot (1-0,70)}{1000}}}  \\\\[2ex] Z&amp;=-4,07\\end{aligned}}\" title=\"Rendered by QuickLaTeX.com\" height=\"195\" width=\"186\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Por outro lado, 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-f4aa318300c46315a36b7bbecbd57e02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_{0,025}=1,96\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"102\" style=\"vertical-align: -6px;\"><\/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\/nivel-de-significancia\/\">N\u00edvel de signific\u00e2ncia 0,05<\/a><\/div>\n<p> Concluindo, o valor absoluto da estat\u00edstica de teste \u00e9 maior que o valor cr\u00edtico, portanto rejeitamos a hip\u00f3tese nula e aceitamos a hip\u00f3tese alternativa. <\/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-06104fc4aa1cf5269aa8bc841cc05a9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|-4,07|=4,07>1,96 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Se rechaza } H_0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;424&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/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-a-media\/\">Teste de hip\u00f3tese para a m\u00e9dia<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-de-hipotesis-para-las-proporciones-de-dos-muestras\"><\/span> Teste de hip\u00f3teses para duas propor\u00e7\u00f5es amostrais<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>O teste de hip\u00f3teses para propor\u00e7\u00f5es de duas amostras<\/strong> \u00e9 usado para rejeitar ou aceitar a hip\u00f3tese nula de que as propor\u00e7\u00f5es de duas popula\u00e7\u00f5es diferentes s\u00e3o iguais.<\/p>\n<p> Assim, a hip\u00f3tese nula de um teste de hip\u00f3tese para propor\u00e7\u00f5es de duas amostras \u00e9 sempre:<\/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-5572e3ad602776be8957247415435ef5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"H_0: p_1=p_2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"93\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Embora a hip\u00f3tese alternativa possa ser uma das tr\u00eas op\u00e7\u00f5es:<\/p>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\begin{array}{l}H_1:p_1\\neq p_2\\\\[2ex]H_1:p_1&gt;p_2\\\\[2ex]H_1:p_1 The combined ratio of the two samples is calculated as follows:[latex]p=\\cfrac {x_1+x_2}{n_1+n_2}\n\n*** Error message:\nMissing $ inserted.\nleading text: \\begin{array}{l}\nPlease use \\mathaccent for accents in math mode.\nleading text: ...H_1:p_1&gt;p_2\\\\[2ex]H_1:p_1 The combined ratio\nPlease use \\mathaccent for accents in math mode.\nleading text: ...\\[2ex]H_1:p_1 The combined ratio of the two\nPlease use \\mathaccent for accents in math mode.\nleading text: ...combined of the two samples is calculated\n\\begin{array} on input line 8 ended by \\end{document}.\nleading text: \\end{document}\nImproper \\prevdepth.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\cr inserted.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nYou can't use `\\end' in internal vertical mode.\n\n<\/pre>\n<p> E a f\u00f3rmula para calcular a estat\u00edstica do teste de hip\u00f3tese para duas propor\u00e7\u00f5es amostrais \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-27dc38fa4280149a55c46c6753204c9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\displaystyle \\frac{x_1}{n_1}-\\frac{x_2}{n_2}}{\\displaystyle \\sqrt{p(1-p)\\left(\\frac{1}{n_1}+\\frac{1}{n_2}\\right)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"94\" width=\"214\" 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 do teste de hip\u00f3tese para propor\u00e7\u00f5es de duas amostras.<\/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-d7aa45c8899989487fb32dab51a8f7d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o n\u00famero de resultados na 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-de02251c2c969c17b8633e299d9a2244_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o n\u00famero de resultados na 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-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 combinada das duas amostras. <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-de-hipotesis-para-las-proporciones-de-k-muestras\"><\/span> Teste de hip\u00f3teses para k propor\u00e7\u00f5es de amostras<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Num <strong>teste de hip\u00f3tese sobre propor\u00e7\u00f5es de k amostras,<\/strong> o objetivo \u00e9 determinar se todas as propor\u00e7\u00f5es das diferentes popula\u00e7\u00f5es s\u00e3o iguais ou, pelo contr\u00e1rio, se existem propor\u00e7\u00f5es diferentes. Portanto, a hip\u00f3tese nula e a hip\u00f3tese alternativa neste caso s\u00e3o:<\/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-77d7e13b427dd927953473a6bfbe9a55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\text{Todas las proporciones son iguales}\\\\[2ex] H_1: \\text{No todas las proporciones son iguales} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"341\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Neste caso, a propor\u00e7\u00e3o combinada de todas as 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-bd6eafe24ac6e33f95c11428cdf34b29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p=\\cfrac{\\displaystyle\\sum_{i=1}^k x_i}{\\displaystyle\\sum_{i=1}^k n_i}=\\cfrac{x_1+x_2+\\dots+x_k}{n_1+n_2+\\dots+n_k}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"250\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p> A f\u00f3rmula para encontrar a estat\u00edstica do teste de hip\u00f3tese para k propor\u00e7\u00f5es amostrais \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-bf14ba17db281bb65549da86f59a0b65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\chi^2 =\\sum_{i=1}^k \\frac{(x_i-e_i)^2}{e_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"146\" style=\"vertical-align: -21px;\"><\/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-7213d98c216b76fca752271158e4c7e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\chi^2 = \\frac{(x_1-e_1)^2}{e_1} +\\frac{(x_2-e_2)^2}{e_2} +\\dots+\\frac{(x_k-e_k)^2}{e_k}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"371\" style=\"vertical-align: -15px;\"><\/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-984dc78529fc235b078a9f3b62d0f0c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a estat\u00edstica do teste de hip\u00f3tese para k propor\u00e7\u00f5es amostrais. Nesse caso, a estat\u00edstica segue uma distribui\u00e7\u00e3o qui-quadrado.<\/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-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 i.<\/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-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>\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 combinada de todas as amostras.<\/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-550848dfdd05b5c6464d4e22fbf52486_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o n\u00famero de acertos esperados da amostra i. \u00c9 calculado multiplicando a propor\u00e7\u00e3o combinada<\/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> por tamanho de amostra<\/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> .<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 o teste de hip\u00f3tese de propor\u00e7\u00e3o nas estat\u00edsticas. Voc\u00ea encontrar\u00e1, portanto, a f\u00f3rmula do teste de hip\u00f3tese da propor\u00e7\u00e3o e, al\u00e9m disso, um exerc\u00edcio passo a passo para entender perfeitamente como isso \u00e9 feito. O que \u00e9 teste de hip\u00f3tese para propor\u00e7\u00e3o? O teste de hip\u00f3tese de propor\u00e7\u00e3o \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-260","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\u00f3teses para propor\u00e7\u00e3o<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 o teste de hip\u00f3tese de propor\u00e7\u00e3o, sua f\u00f3rmula e um exemplo concreto de teste de hip\u00f3tese de propor\u00e7\u00e3o.\" \/>\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-proporcao\/\" \/>\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\u00f3teses para propor\u00e7\u00e3o\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 o teste de hip\u00f3tese de propor\u00e7\u00e3o, sua f\u00f3rmula e um exemplo concreto de teste de hip\u00f3tese de propor\u00e7\u00e3o.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-proporcao\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T11:07:43+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e2f5ad36dae72cd89279809ab3ea6d20_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=\"5 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-proporcao\/\",\"url\":\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-proporcao\/\",\"name\":\"\u25b7 Teste de hip\u00f3teses para propor\u00e7\u00e3o\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T11:07:43+00:00\",\"dateModified\":\"2023-08-03T11:07:43+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 de propor\u00e7\u00e3o, sua f\u00f3rmula e um exemplo concreto de teste de hip\u00f3tese de propor\u00e7\u00e3o.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-proporcao\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-proporcao\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-proporcao\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Teste de hip\u00f3tese 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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