{"id":283,"date":"2023-08-03T03:11:14","date_gmt":"2023-08-03T03:11:14","guid":{"rendered":"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-a-diferenca-de-medias\/"},"modified":"2023-08-03T03:11:14","modified_gmt":"2023-08-03T03:11:14","slug":"teste-de-hipotese-para-a-diferenca-de-medias","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-a-diferenca-de-medias\/","title":{"rendered":"Teste de hip\u00f3teses para diferen\u00e7a de m\u00e9dias"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 o teste de hip\u00f3tese de diferen\u00e7a de m\u00e9dias nas estat\u00edsticas e para que ele \u00e9 usado. Da mesma forma, voc\u00ea descobrir\u00e1 como fazer um teste de hip\u00f3tese sobre a diferen\u00e7a de m\u00e9dias e um exerc\u00edcio resolvido 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-medias\"><\/span> O que \u00e9 teste de hip\u00f3tese para diferen\u00e7a m\u00e9dia?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>O teste de hip\u00f3teses para diferen\u00e7a de m\u00e9dias<\/strong> \u00e9 um teste estat\u00edstico usado para rejeitar ou aceitar a hip\u00f3tese de que as m\u00e9dias de duas popula\u00e7\u00f5es s\u00e3o diferentes. Ou seja, o teste de hip\u00f3tese de diferen\u00e7a de m\u00e9dias \u00e9 usado para determinar se as m\u00e9dias de duas popula\u00e7\u00f5es s\u00e3o iguais ou diferentes.<\/p>\n<p> Tenha em mente que as decis\u00f5es tomadas em testes de hip\u00f3teses s\u00e3o baseadas em um <a href=\"https:\/\/statorials.org\/pt\/um-nivel-de-confianca\/\">n\u00edvel de confian\u00e7a<\/a> previamente estabelecido, portanto n\u00e3o se pode garantir que o resultado de um teste de hip\u00f3teses esteja sempre correto, mas sim que \u00e9 o resultado mais prov\u00e1vel que seja verdadeiro.<\/p>\n<p> O teste de hip\u00f3teses para a diferen\u00e7a de duas m\u00e9dias 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 veremos como realizar um teste de hip\u00f3tese para a diferen\u00e7a de m\u00e9dias.<\/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\/distribuicao-amostral-da-diferenca-de-medias\/\">Distribui\u00e7\u00e3o amostral de 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-medias\"><\/span> F\u00f3rmula de teste de hip\u00f3teses para diferen\u00e7a de m\u00e9dias<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A f\u00f3rmula que deve ser usada para testar hip\u00f3teses sobre a diferen\u00e7a de m\u00e9dias varia dependendo se as vari\u00e2ncias populacionais s\u00e3o conhecidas e, se n\u00e3o, se podem ser consideradas iguais ou diferentes. Portanto, nesta se\u00e7\u00e3o veremos qual f\u00f3rmula usar dependendo do caso.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-conocidas\"><\/span> Varia\u00e7\u00f5es conhecidas<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>A f\u00f3rmula para calcular a estat\u00edstica do teste de hip\u00f3tese para a diferen\u00e7a de m\u00e9dias quando as vari\u00e2ncias s\u00e3o conhecidas<\/strong> \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-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 de teste de hip\u00f3tese 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<p> Lembre-se que este \u00e9 o caso menos comum, portanto esta f\u00f3rmula s\u00f3 \u00e9 utilizada em alguns casos espec\u00edficos.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-desconocidas-e-iguales\"><\/span> Desvios desconhecidos e iguais<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>A f\u00f3rmula para calcular a estat\u00edstica do teste de hip\u00f3tese para a diferen\u00e7a nas m\u00e9dias quando as vari\u00e2ncias da popula\u00e7\u00e3o s\u00e3o desconhecidas, mas consideradas iguais<\/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-b879974c3d05ebcb049125dbaf9f0a48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle (\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle s_p\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"67\" width=\"197\" 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-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a estat\u00edstica de teste de hip\u00f3tese para a diferen\u00e7a de m\u00e9dias com vari\u00e2ncias desconhecidas, que segue uma distribui\u00e7\u00e3o t de Student com n <sub>1<\/sub> + n <sub>2<\/sub> -2 graus de liberdade.<\/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-db24109a40d5779feee64c7bccc11371_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_p\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"15\" style=\"vertical-align: -6px;\"><\/p>\n<p> \u00e9 o desvio padr\u00e3o combinado.<\/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<p> O desvio padr\u00e3o combinado das duas amostras \u00e9 calculado com a seguinte f\u00f3rmula: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a8fb43d179e453d19f5781319aa9e1ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle s_p=\\sqrt{\\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"240\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-desconocidas-y-diferentes\"><\/span> Varia\u00e7\u00f5es desconhecidas e diferentes<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Quando as vari\u00e2ncias populacionais s\u00e3o desconhecidas e, al\u00e9m disso, s\u00e3o assumidas como diferentes, a f\u00f3rmula para calcular a estat\u00edstica do teste de hip\u00f3tese para a diferen\u00e7a de m\u00e9dias<\/strong> \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-01c79415ff9c173fa4517d4b1a859a8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle (\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle \\sqrt{\\frac{s_1^2}{n_1}+\\frac{s_2^2}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"197\" 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-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a estat\u00edstica de teste de hip\u00f3tese para a diferen\u00e7a de m\u00e9dias com vari\u00e2ncias desconhecidas, que segue a distribui\u00e7\u00e3o t de Student.<\/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<p> Por\u00e9m, neste caso, os graus de liberdade da distribui\u00e7\u00e3o t de Student s\u00e3o calculados pela seguinte f\u00f3rmula: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ecf1ccfa1ecb47b889c569e5faa65a78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle GL=\\frac{\\displaystyle\\left(\\frac{s_1^2}{n_1}+\\frac{s_2^2}{n_2}\\right)^2}{\\displaystyle\\frac{\\displaystyle\\frac{s_1^2}{n_1}}{n_1-1}+\\frac{\\displaystyle\\frac{s_2^2}{n_2}}{n_2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"115\" width=\"180\" style=\"vertical-align: -61px;\"><\/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\/intervalo-de-confianca-para-a-diferenca-de-medias\/\">F\u00f3rmula de intervalo de confian\u00e7a para diferen\u00e7a de m\u00e9dias<\/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-medias\"><\/span> Exemplo concreto de teste de hip\u00f3tese para a diferen\u00e7a de m\u00e9dias<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Para finalizar a assimila\u00e7\u00e3o do conceito de teste de hip\u00f3teses sobre diferen\u00e7a de m\u00e9dias, veremos um exemplo concreto desse tipo de teste de hip\u00f3teses.<\/p>\n<ul>\n<li> Voc\u00ea deseja fazer um estudo estat\u00edstico sobre o sal\u00e1rio de duas empresas concorrentes, mais especificamente, deseja determinar se o sal\u00e1rio m\u00e9dio das duas empresas \u00e9 diferente. Para isso, s\u00e3o retiradas uma amostra de 47 trabalhadores de uma empresa e outra amostra de 55 trabalhadores da outra empresa. Um sal\u00e1rio m\u00e9dio de US$ 40.000 e um desvio padr\u00e3o de US$ 12.000 s\u00e3o obtidos da primeira amostra, enquanto um sal\u00e1rio m\u00e9dio de US$ 46.000 e um desvio padr\u00e3o de US$ 18.000 s\u00e3o obtidos da segunda amostra. Realize um teste de hip\u00f3tese com n\u00edvel de signific\u00e2ncia de 5% para determinar se os sal\u00e1rios m\u00e9dios s\u00e3o diferentes ou n\u00e3o.<\/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 diferen\u00e7a das duas m\u00e9dias s\u00e3o as seguintes:<\/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-4dd9e80c0a87987d689d7b8d99be9d90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu_1-\\mu_2=0\\\\[2ex] H_1:\\mu_1-\\mu_2\\neq 0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"141\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Neste caso, as disparidades populacionais n\u00e3o s\u00e3o conhecidas, mas pode-se presumir que s\u00e3o iguais porque s\u00e3o empresas concorrentes e as condi\u00e7\u00f5es de trabalho do mercado em que operam s\u00e3o muito semelhantes. Portanto, a f\u00f3rmula para a estat\u00edstica de teste de hip\u00f3tese para a diferen\u00e7a de m\u00e9dias que devemos usar \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-b879974c3d05ebcb049125dbaf9f0a48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle (\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle s_p\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"67\" width=\"197\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p> Portanto, calculamos o desvio padr\u00e3o combinado 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-0308363d68c4677761d44b214b1609d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle s_p&amp;=\\sqrt{\\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}\\\\[2ex]\\displaystyle s_p&amp;=\\sqrt{\\frac{(47-1)\\cdot 12000^2+(55-1)\\cdot 18000^2}{47+55-2}}\\\\[2ex]s_p&amp;=15530,61\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"161\" width=\"337\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Aplicamos agora a f\u00f3rmula de teste de hip\u00f3tese para a diferen\u00e7a de m\u00e9dias:<\/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-c5bf7791d156d1d7593182a7ffc64417_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle (\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle s_p\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}=\\cfrac{(40000-46000)-0}{\\displaystyle 15530,61\\sqrt{\\frac{1}{47}+\\frac{1}{55}}}=-1,94\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"451\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p> Por outro lado, procuramos o valor cr\u00edtico do teste de hip\u00f3tese para a diferen\u00e7a de m\u00e9dias na <a href=\"https:\/\/statorials.org\/pt\/tabela-de-distribuicao-t-do-aluno\/\">tabela t de Student<\/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-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-d5f11ecd0336e50c63b0ab2fab4bd530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}t_{\\alpha\/2| n_1+n_2-2}= \\ \\color{orange}\\bm{?}\\\\[4ex]t_{0,025| 100}=1,984\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"72\" width=\"184\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Ent\u00e3o, como o valor absoluto da estat\u00edstica de teste \u00e9 menor que o valor cr\u00edtico do teste, a hip\u00f3tese nula \u00e9 aceita e a hip\u00f3tese alternativa \u00e9 rejeitada.<\/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-ca4a2499b93203ce31a36a1cbacbcc8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|-1,94|=1,94<1,984 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Se rechaza } H_1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"432\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 o teste de hip\u00f3tese de diferen\u00e7a de m\u00e9dias nas estat\u00edsticas e para que ele \u00e9 usado. Da mesma forma, voc\u00ea descobrir\u00e1 como fazer um teste de hip\u00f3tese sobre a diferen\u00e7a de m\u00e9dias e um exerc\u00edcio resolvido passo a passo. O que \u00e9 teste de hip\u00f3tese para diferen\u00e7a m\u00e9dia? O [&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-283","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 m\u00e9dias<\/title>\n<meta name=\"description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 o teste de hip\u00f3tese para diferen\u00e7a de m\u00e9dias, como ele \u00e9 realizado (f\u00f3rmula) e um exemplo resolvido passo a passo.\" \/>\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-a-diferenca-de-medias\/\" \/>\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 m\u00e9dias\" \/>\n<meta property=\"og:description\" content=\"Aqui voc\u00ea encontrar\u00e1 o que \u00e9 o teste de hip\u00f3tese para diferen\u00e7a de m\u00e9dias, como ele \u00e9 realizado (f\u00f3rmula) e um exemplo resolvido passo a passo.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-a-diferenca-de-medias\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T03:11:14+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0b7968d96046c1f555a7c95e7c3c408e_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-a-diferenca-de-medias\/\",\"url\":\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-a-diferenca-de-medias\/\",\"name\":\"\u25b7 Teste de hip\u00f3tese para diferen\u00e7a de m\u00e9dias\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-08-03T03:11:14+00:00\",\"dateModified\":\"2023-08-03T03:11:14+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 m\u00e9dias, como ele \u00e9 realizado (f\u00f3rmula) e um exemplo resolvido passo a passo.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-a-diferenca-de-medias\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-a-diferenca-de-medias\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/teste-de-hipotese-para-a-diferenca-de-medias\/#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 de m\u00e9dias\"}]},{\"@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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