{"id":287,"date":"2023-08-03T01:52:23","date_gmt":"2023-08-03T01:52:23","guid":{"rendered":"https:\/\/statorials.org\/pt\/teste-z\/"},"modified":"2023-08-03T01:52:23","modified_gmt":"2023-08-03T01:52:23","slug":"teste-z","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/teste-z\/","title":{"rendered":"Teste z"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 o teste Z em estat\u00edstica e para que \u00e9 usado. Voc\u00ea descobrir\u00e1, portanto, como fazer um teste Z, as diferentes f\u00f3rmulas do teste Z e, finalmente, a diferen\u00e7a entre o teste Z e outros testes estat\u00edsticos.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-prueba-z\"><\/span>O que \u00e9 um teste Z?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Em estat\u00edstica, o <strong>teste Z<\/strong> \u00e9 um teste de hip\u00f3tese usado quando a estat\u00edstica do teste segue uma distribui\u00e7\u00e3o normal. A estat\u00edstica obtida de um teste Z \u00e9 chamada de estat\u00edstica Z ou valor Z.<\/p>\n<p> A f\u00f3rmula do teste Z \u00e9 sempre a mesma, mais precisamente, a estat\u00edstica do teste Z \u00e9 igual \u00e0 diferen\u00e7a entre o valor amostral calculado e o valor populacional proposto dividido pelo desvio padr\u00e3o do par\u00e2metro populacional.<\/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-5ad1fab5e2c6a8d32ae02f2e2d16d42c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\widehat{X}-X}{\\sigma_{_X}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"92\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> O teste Z \u00e9 usado para rejeitar ou aceitar a hip\u00f3tese nula de testes de hip\u00f3teses nos quais a estat\u00edstica do teste segue uma distribui\u00e7\u00e3o normal.<\/p>\n<p> Por exemplo, o teste Z \u00e9 usado para testar a hip\u00f3tese da m\u00e9dia quando a vari\u00e2ncia populacional \u00e9 conhecida, a fim de rejeitar ou aceitar uma hip\u00f3tese sobre o valor da m\u00e9dia populacional. <\/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-1\/\">O que \u00e9 teste de hip\u00f3tese?<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-pruebas-z\"><\/span> Tipos de testes Z<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Diferentes tipos de testes Z podem ser distinguidos dependendo do par\u00e2metro no qual o teste de hip\u00f3tese \u00e9 realizado:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Teste Z para m\u00e9dia.<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Teste Z para propor\u00e7\u00e3o.<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Teste Z para diferen\u00e7a de m\u00e9dias.<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Teste Z para diferen\u00e7a de propor\u00e7\u00f5es.<\/strong><\/span><\/li>\n<\/ul>\n<p> Abaixo voc\u00ea confere a f\u00f3rmula para cada tipo de teste Z.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-media\"><\/span> Teste Z para m\u00e9dia<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A <strong>f\u00f3rmula do teste Z para a m\u00e9dia<\/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-fdf1817a07bfb8c1eda9a8d8ccd8c828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{\\sigma}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"81\" style=\"vertical-align: -34px;\"><\/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 Z para a m\u00e9dia.<\/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-a39858a792fb4fe9a3173e004701f2a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a m\u00e9dia 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-05d9eae892416bd34247a25207f8b718_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 o valor m\u00e9dio proposto.<\/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-eaaf379fee5e67946f3fedf5631047b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o desvio padr\u00e3o da popula\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-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<\/ul>\n<p> Uma vez calculada a estat\u00edstica do teste de hip\u00f3tese para a m\u00e9dia, o resultado deve ser interpretado para rejeitar ou rejeitar a hip\u00f3tese nula:<\/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 m\u00e9dia 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 m\u00e9dia corresponder \u00e0 cauda direita, a hip\u00f3tese nula ser\u00e1 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 m\u00e9dia corresponder \u00e0 cauda esquerda, a hip\u00f3tese nula ser\u00e1 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-0e2ccadfc369eb7543b8f86dfccc528e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: \\mu\\neq \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |Z|>Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_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=\"440\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Os valores cr\u00edticos do teste Z s\u00e3o obtidos na tabela de distribui\u00e7\u00e3o normal padr\u00e3o. <\/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<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-proporcion\"><\/span> Teste Z para propor\u00e7\u00e3o<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A <strong>f\u00f3rmula do teste Z para 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-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 Z para 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 Z para a propor\u00e7\u00e3o, mas \u00e9 preciso ent\u00e3o interpretar o resultado obtido:<\/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<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-proporcao\/\">Teste de hip\u00f3tese para propor\u00e7\u00e3o<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-diferencia-de-medias\"><\/span> Teste Z para diferen\u00e7a de m\u00e9dias<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>A f\u00f3rmula para calcular a estat\u00edstica do teste Z para a diferen\u00e7a de<\/strong> m\u00e9dias \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-0b7968d96046c1f555a7c95e7c3c408e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\displaystyle (\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"203\" 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 Z para a diferen\u00e7a de duas m\u00e9dias com vari\u00e2ncia conhecida, que segue uma distribui\u00e7\u00e3o normal padr\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-776e8d37515f607d16b6ea33cf27cb8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a m\u00e9dia 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-eed6e51baac07f2aaf1c82b4b328ded8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a m\u00e9dia 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-1436bb55d331d1efe559fd1e55245851_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 a m\u00e9dia 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-f06b28a75570ecb4df1371dea2d9f2b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 a m\u00e9dia 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-802bfc799b8f222d7b47270e1569770b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o desvio padr\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-063ad2fadbc81bd1df35589566b0bd16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o desvio padr\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-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<\/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\/teste-de-hipotese-para-a-diferenca-de-medias\/\">Teste de hip\u00f3teses para a diferen\u00e7a de m\u00e9dias<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-diferencia-de-proporciones\"><\/span> Teste Z para diferen\u00e7a de propor\u00e7\u00f5es<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A <strong>f\u00f3rmula para calcular a estat\u00edstica do teste Z 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 do teste Z 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\/teste-de-hipotese-para-diferenca-em-proporcoes\/\">Teste de hip\u00f3teses para diferen\u00e7a em propor\u00e7\u00f5es<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hacer-una-prueba-z\"><\/span>Como fazer um teste Z<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agora que vimos quais s\u00e3o as diferentes f\u00f3rmulas do teste Z, vamos ver como realizar um teste Z.<\/p>\n<p> As etapas para realizar um teste Z s\u00e3o as seguintes.<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Defina a <a href=\"https:\/\/statorials.org\/pt\/hipotese-nula-e-alternativa\/\">hip\u00f3tese nula e a hip\u00f3tese alternativa<\/a> de teste de hip\u00f3tese.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Decida o <a href=\"https:\/\/statorials.org\/pt\/nivel-de-significancia\/\">n\u00edvel de signific\u00e2ncia alfa (\u03b1)<\/a> do teste de hip\u00f3tese.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Verifique se os requisitos para usar o teste Z foram atendidos.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Aplique a f\u00f3rmula do teste Z correspondente e calcule a estat\u00edstica do teste.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Interprete o resultado do teste Z comparando-o com o valor cr\u00edtico do teste.<\/span><\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-y-prueba-t\"><\/span>Teste Z e teste t<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Por fim, veremos qual a diferen\u00e7a entre o teste Z e o teste t, pois s\u00e3o certamente os dois tipos de testes de hip\u00f3teses mais utilizados em estat\u00edstica.<\/p>\n<p> O <strong>teste t<\/strong> , tamb\u00e9m chamado <strong>de teste t de Student<\/strong> , \u00e9 um teste de hip\u00f3tese usado quando a popula\u00e7\u00e3o em estudo segue uma distribui\u00e7\u00e3o normal, mas o tamanho da amostra \u00e9 muito pequeno para saber a vari\u00e2ncia da popula\u00e7\u00e3o.<\/p>\n<p> Portanto, <strong>a principal diferen\u00e7a entre usar o teste Z e o teste t<\/strong> \u00e9 se a vari\u00e2ncia \u00e9 conhecida ou n\u00e3o. Quando a vari\u00e2ncia populacional \u00e9 conhecida, utiliza-se o teste Z, enquanto quando a vari\u00e2ncia populacional \u00e9 desconhecida, utiliza-se o teste t. <\/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-t-do-aluno\/\">teste t (estat\u00edsticas)<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 o teste Z em estat\u00edstica e para que \u00e9 usado. Voc\u00ea descobrir\u00e1, portanto, como fazer um teste Z, as diferentes f\u00f3rmulas do teste Z e, finalmente, a diferen\u00e7a entre o teste Z e outros testes estat\u00edsticos. O que \u00e9 um teste Z? Em estat\u00edstica, o teste Z \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-287","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>\u25b7Teste Z<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea descobrir\u00e1 o que \u00e9 o teste Z em estat\u00edstica, como fazer um teste Z (f\u00f3rmula) e exemplos resolvidos do teste Z.\" \/>\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-z\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7Teste Z\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea descobrir\u00e1 o que \u00e9 o teste Z em estat\u00edstica, como fazer um teste Z (f\u00f3rmula) e exemplos resolvidos do teste Z.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/teste-z\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T01:52:23+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5ad1fab5e2c6a8d32ae02f2e2d16d42c_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-z\/\",\"url\":\"https:\/\/statorials.org\/pt\/teste-z\/\",\"name\":\"\u25b7Teste Z\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T01:52:23+00:00\",\"dateModified\":\"2023-08-03T01:52:23+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Aqui voc\u00ea descobrir\u00e1 o que \u00e9 o teste Z em estat\u00edstica, como fazer um teste Z (f\u00f3rmula) e exemplos resolvidos do teste Z.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/teste-z\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/teste-z\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/teste-z\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Teste z\"}]},{\"@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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