{"id":293,"date":"2023-08-03T00:39:59","date_gmt":"2023-08-03T00:39:59","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%ad%a6%e7%94%9ft%e6%a3%80%e9%aa%8c\/"},"modified":"2023-08-03T00:39:59","modified_gmt":"2023-08-03T00:39:59","slug":"%e5%ad%a6%e7%94%9ft%e6%a3%80%e9%aa%8c","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%ad%a6%e7%94%9ft%e6%a3%80%e9%aa%8c\/","title":{"rendered":"\u5b66\u751f t \u68c0\u9a8c"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u5b66\u751f t \u68c0\u9a8c\u4ee5\u53ca\u5b83\u5728\u7edf\u8ba1\u5b66\u4e2d\u7684\u7528\u9014\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8fdb\u884c Student t \u68c0\u9a8c\u3001Student t \u68c0\u9a8c\u6709\u54ea\u4e9b\u4e0d\u540c\u7c7b\u578b\u4ee5\u53ca\u6bcf\u79cd\u7c7b\u578b\u7684\u516c\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-prueba-t-de-student\"><\/span>\u4ec0\u4e48\u662f\u5b66\u751f t \u68c0\u9a8c\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5b66\u751f t \u68c0\u9a8c<\/strong>\uff0c\u4e5f\u79f0\u4e3a<strong>T \u68c0\u9a8c<\/strong>\u6216\u7b80\u79f0<strong>t \u68c0\u9a8c<\/strong>\uff0c\u662f\u4e00\u79cd\u7edf\u8ba1\u68c0\u9a8c\uff0c\u5176\u4e2d\u68c0\u9a8c\u7edf\u8ba1\u91cf\u9075\u5faa<a href=\"https:\/\/statorials.org\/cn\/\u5b66\u751f\u5206\u5e03\/\">\u5b66\u751f t \u5206\u5e03<\/a>\u3002\u56e0\u6b64\uff0c\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u5b66\u751f t \u68c0\u9a8c\u7528\u4e8e\u62d2\u7edd\u6216\u63a5\u53d7\u5047\u8bbe\u68c0\u9a8c\u7684\u539f\u5047\u8bbe\u3002<\/p>\n<p>\u5177\u4f53\u6765\u8bf4\uff0c\u5b66\u751f t \u68c0\u9a8c\u7528\u4e8e<a href=\"https:\/\/statorials.org\/cn\/\u5047\u8bbe\u68c0\u9a8c1\/\">\u5047\u8bbe\u68c0\u9a8c<\/a>\uff0c\u5176\u4e2d\u6240\u7814\u7a76\u7684\u603b\u4f53\u9075\u5faa\u6b63\u6001\u5206\u5e03\uff0c\u4f46\u6837\u672c\u91cf\u592a\u5c0f\u800c\u65e0\u6cd5\u4e86\u89e3\u603b\u4f53\u65b9\u5dee\u3002<\/p>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0cStudent&#8217;s t \u68c0\u9a8c\u7528\u4e8e\u62d2\u7edd\u6216\u63a5\u53d7\u67d0\u4e9b\u5047\u8bbe\u68c0\u9a8c\u7684\u7814\u7a76\u5047\u8bbe\u3002\u4f8b\u5982\uff0c\u5b66\u751f t \u68c0\u9a8c\u7528\u4e8e\u68c0\u9a8c\u4e00\u4e2a\u6837\u672c\u3001\u72ec\u7acb\u6837\u672c\u6216\u76f8\u5173\u6837\u672c\u7684\u5047\u8bbe\u3002\u7136\u540e\u6211\u4eec\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u6bcf\u79cd\u60c5\u51b5\u4e0b\u7684\u5b66\u751f t \u68c0\u9a8c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-pruebas-t-de-student\"><\/span>\u5b66\u751f t \u68c0\u9a8c\u7684\u7c7b\u578b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5b66\u751f t \u68c0\u9a8c\u5206\u4e3a\u4e09\u79cd\u7c7b\u578b<\/strong>\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u5355\u6837\u672c\u5b66\u751f t \u68c0\u9a8c<\/strong>\u2013 \u7528\u4e8e\u68c0\u9a8c\u6709\u5173\u6837\u672c\u5747\u503c\u7684\u5047\u8bbe\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u4e24\u4e2a\u72ec\u7acb\u6837\u672c\u7684\u5b66\u751f t \u68c0\u9a8c<\/strong>\uff1a\u5b83\u5141\u8bb8\u60a8\u68c0\u9a8c\u4e24\u4e2a\u72ec\u7acb\u6837\u672c\u5747\u503c\u4e4b\u95f4\u5dee\u5f02\u7684\u5047\u8bbe\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u4e24\u4e2a\u914d\u5bf9\u6837\u672c\uff08\u6216\u76f8\u5173\u6837\u672c\uff09\u7684\u5b66\u751f t \u68c0\u9a8c<\/strong>&#8211; \u7528\u4e8e\u8c03\u67e5\u6709\u5173\u4e24\u6b21\u6d4b\u8bd5\u6837\u672c\u5e73\u5747\u503c\u7684\u5047\u8bbe\u3002<\/span> <\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-t-de-student-para-una-muestra\"><\/span>\u5b66\u751f t \u68c0\u9a8c\u6837\u672c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u6837\u672c\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\u662f\u6307\u68c0\u9a8c\u7684\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\u8bf4\u660e\u603b\u4f53\u5747\u503c\u7684\u503c\u7684\u60c5\u51b5\u3002<\/p>\n<p><strong>\u5355\u6837\u672c\u5b66\u751f t \u68c0\u9a8c\u7684\u516c\u5f0f<\/strong>\u5982\u4e0b\uff1a<\/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-f8277d83b2d28325f25f5d118486200f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{s}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"75\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\">\u91d1\u5b50\uff1a<\/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>\u662f\u5e73\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u7531\u5b66\u751f t \u5206\u5e03\u5b9a\u4e49\u3002<\/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>\u662f\u6837\u672c\u5747\u503c\u3002<\/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>\u662f\u5047\u8bbe\u68c0\u9a8c\u4e2d\u63d0\u51fa\u7684\u5e73\u5747\u503c\u3002<\/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-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u6837\u672c\u6807\u51c6\u5dee\u3002<\/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>\u662f\u6837\u672c\u5927\u5c0f\u3002<\/li>\n<\/ul>\n<p>\u8ba1\u7b97\u51fa\u5b66\u751f t \u68c0\u9a8c\u7684\u503c\u540e\uff0c\u5fc5\u987b\u5c06\u5177\u6709\u4e34\u754c\u503c\u7684\u7edf\u8ba1\u68c0\u9a8c\u7ed3\u679c\u89e3\u91ca\u4e3a\u662f\u5426\u62d2\u7edd\u539f\u5047\u8bbe\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\u662f\u53cc\u5411\u7684\uff0c\u5e76\u4e14\u5b66\u751f t \u68c0\u9a8c\u7684\u7edd\u5bf9\u503c\u5927\u4e8e\u4e34\u754c\u503c t <sub>\u03b1\/2|n-1 \uff0c<\/sub>\u5219\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\u4e0e\u53f3\u5c3e\u5339\u914d\uff0c\u5e76\u4e14\u5b66\u751f\u7684 t \u68c0\u9a8c\u503c\u5927\u4e8e\u4e34\u754c\u503c t <sub>\u03b1|n-1<\/sub> \uff0c\u5219\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u5e73\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\u4e0e\u5de6\u5c3e\u5339\u914d\uff0c\u5e76\u4e14\u5b66\u751f\u7684 t \u68c0\u9a8c\u503c\u5c0f\u4e8e\u4e34\u754c\u503c -t <sub>\u03b1|n-1<\/sub> \uff0c\u5219\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/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-31fb206b75a47181c7c673f54ba28ee8_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 } |t|>t_{\\alpha\/2|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t>t_{\\alpha|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t<-t_{\\alpha|n-1} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"457\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u5173\u952e\u6d4b\u8bd5\u503c\u662f\u4ece\u5b66\u751f\u5206\u5e03\u8868\u4e2d\u83b7\u5f97\u7684\u3002 <\/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>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u5e73\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\/\">\u5747\u503c\u5047\u8bbe\u68c0\u9a8c\u7684\u5177\u4f53\u793a\u4f8b<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-t-de-student-para-muestras-independientes\"><\/span>\u72ec\u7acb\u6837\u672c\u7684\u5b66\u751f t \u68c0\u9a8c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u72ec\u7acb\u6837\u672c\u7684\u5b66\u751f t \u68c0\u9a8c\u7528\u4e8e\u62d2\u7edd\u6216\u63a5\u53d7\u4e24\u4e2a\u603b\u4f53\u5747\u503c\u4e4b\u95f4\u5b58\u5728\u5173\u7cfb\u7684\u5047\u8bbe\uff0c\u4f8b\u5982\u4e24\u4e2a\u603b\u4f53\u7684\u5747\u503c\u4e0d\u540c\u6216\u603b\u4f53 A \u7684\u5747\u503c\u5927\u4e8e\u3002\u4eba\u53e3 B .<\/p>\n<p>\u4f46\u662f\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u5b66\u751f t \u68c0\u9a8c\u516c\u5f0f\u4f1a\u6839\u636e\u603b\u4f53\u65b9\u5dee\u662f\u5426\u53ef\u4ee5\u5047\u8bbe\u76f8\u7b49\u800c\u53d8\u5316\u3002\u7136\u540e\u6211\u4eec\u5c06\u770b\u5230\u4e24\u79cd\u53ef\u80fd\u7684\u60c5\u51b5\u3002<\/p>\n<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-desconocidas-e-iguales\"><\/span>\u672a\u77e5\u4e14\u76f8\u7b49\u7684\u504f\u5dee<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>\u5f53\u603b\u4f53\u65b9\u5dee\u672a\u77e5\u4f46\u5047\u8bbe\u76f8\u7b49\u65f6\uff0c\u8ba1\u7b97\u72ec\u7acb\u6837\u672c\u7684 Student t \u68c0\u9a8c\u7684\u516c\u5f0f<\/strong>\u5982\u4e0b\uff1a<\/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\">\u91d1\u5b50\uff1a<\/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>\u662f\u65b9\u5dee\u672a\u77e5\u7684\u5747\u503c\u5dee\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u9075\u5faa\u81ea\u7531\u5ea6\u4e3a n <sub>1<\/sub> + n <sub>2<\/sub> -2 \u7684 Student t \u5206\u5e03\u3002<\/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>\u662f\u603b\u4f53 1 \u7684\u5e73\u5747\u503c\u3002<\/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>\u662f\u603b\u4f53 2 \u7684\u5e73\u5747\u503c\u3002<\/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>\u662f\u6837\u672c 1 \u7684\u5e73\u5747\u503c\u3002<\/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>\u662f\u6837\u672c 2 \u7684\u5e73\u5747\u503c\u3002<\/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>\u662f\u6c47\u603b\u6807\u51c6\u5dee\u3002<\/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>\u662f\u6837\u672c\u91cf 1\u3002<\/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>\u662f\u6837\u672c\u91cf 2\u3002<\/li>\n<\/ul>\n<p>\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u4e24\u4e2a\u6837\u672c\u7684\u7ec4\u5408\u6807\u51c6\u5dee\uff1a <\/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<h4 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-desconocidas-y-diferentes\"><\/span>\u672a\u77e5\u548c\u4e0d\u540c\u7684\u53d8\u5316<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>\u5f53\u603b\u4f53\u65b9\u5dee\u672a\u77e5\u4e14\u5047\u8bbe\u4e0d\u540c\u65f6\uff0c\u72ec\u7acb\u6837\u672c\u7684 Student t \u68c0\u9a8c\u8ba1\u7b97\u516c\u5f0f<\/strong>\u5982\u4e0b\uff1a<\/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\">\u91d1\u5b50\uff1a<\/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>\u662f\u65b9\u5dee\u672a\u77e5\u7684\u5747\u503c\u5dee\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u9075\u5faa Student t \u5206\u5e03\u3002<\/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>\u662f\u603b\u4f53 1 \u7684\u5e73\u5747\u503c\u3002<\/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>\u662f\u603b\u4f53 2 \u7684\u5e73\u5747\u503c\u3002<\/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>\u662f\u6837\u672c 1 \u7684\u5e73\u5747\u503c\u3002<\/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>\u662f\u6837\u672c 2 \u7684\u5e73\u5747\u503c\u3002<\/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>\u662f\u603b\u4f53 1 \u7684\u6807\u51c6\u5dee\u3002<\/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>\u662f\u603b\u4f53 2 \u7684\u6807\u51c6\u5dee\u3002<\/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>\u662f\u6837\u672c\u91cf 1\u3002<\/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>\u662f\u6837\u672c\u91cf 2\u3002<\/li>\n<\/ul>\n<p>\u4f46\u662f\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0cStudent t \u5206\u5e03\u7684\u81ea\u7531\u5ea6\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\uff1a <\/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>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c\/\">\u5747\u503c\u5dee\u5f02\u5047\u8bbe\u68c0\u9a8c\u7684\u5177\u4f53\u793a\u4f8b<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-t-de-student-para-muestras-pareadas-o-relacionadas\"><\/span>\u914d\u5bf9\u6216\u76f8\u5173\u6837\u672c\u7684\u5b66\u751f t \u68c0\u9a8c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5f53\u6240\u7814\u7a76\u7684\u4e24\u4e2a\u6837\u672c\u5f7c\u6b64\u76f8\u5173\u65f6\u4f7f\u7528\u6b64\u68c0\u9a8c\uff0c\u56e0\u6b64\u5b83\u5b9e\u9645\u4e0a\u662f\u5df2\u5206\u6790\u4e24\u6b21\u7684\u4e2a\u4f53\u7684\u5355\u4e2a\u6837\u672c\uff08\u6bcf\u6b21\u5728\u4e0d\u540c\u7684\u6761\u4ef6\u4e0b\uff09\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u60a8\u53ef\u4ee5\u5206\u6790\u5b66\u751f\u5728\u6570\u5b66\u548c\u7edf\u8ba1\u5b66\u8bfe\u7a0b\u4e2d\u7684\u6210\u7ee9\uff0c\u770b\u770b\u4e24\u4e2a\u79d1\u76ee\u7684\u5e73\u5747\u503c\u4e4b\u95f4\u662f\u5426\u5b58\u5728\u663e\u7740\u5dee\u5f02\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6bcf\u4e2a\u5b66\u751f\u7684\u6570\u5b66\u6210\u7ee9\u90fd\u4e0e\u8be5\u5b66\u751f\u7684\u7edf\u8ba1\u6210\u7ee9\u76f8\u5173\u8054\u3002<\/p>\n<p><strong>\u914d\u5bf9\u6216\u76f8\u5173\u6837\u672c\u7684\u5b66\u751f t \u68c0\u9a8c\u516c\u5f0f<\/strong>\u4e3a\uff1a<\/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-8dd7c22ea301c71dac72ee39ce2e1972_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\overline{x_D}-\\mu_D}{\\displaystyle \\frac{s_D}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"100\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\">\u91d1\u5b50\uff1a<\/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>\u662f\u914d\u5bf9\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u7531\u5b66\u751f t \u5206\u5e03\u5b9a\u4e49\u3002<\/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-aa774a67ebe93af6717679d0fca9e8b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_D}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"23\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u7531\u6570\u636e\u5dee\u5f02\u5f62\u6210\u7684\u6837\u672c\u7684\u5e73\u5747\u503c\u3002<\/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-2df477ea5937645e4858aa3fdc9d699a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_D\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u5047\u8bbe\u68c0\u9a8c\u4e2d\u63d0\u51fa\u7684\u5e73\u5747\u503c\u3002<\/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-67e59a42de9fb7b544e3bbd8030feba5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_D\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"19\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u7531\u6570\u636e\u5dee\u5f02\u5f62\u6210\u7684\u6837\u672c\u7684\u6807\u51c6\u5dee\u3002<\/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>\u662f\u6837\u672c\u5927\u5c0f\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"asunciones-de-la-prueba-t-de-student\"><\/span>\u5b66\u751f\u7684 t \u68c0\u9a8c\u5047\u8bbe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u8fdb\u884c\u5b66\u751f t \u68c0\u9a8c\uff0c\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u8fde\u7eed\u6027<\/strong>\u2014\u2014\u6837\u672c\u6570\u636e\u662f\u8fde\u7eed\u7684\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u968f\u673a\u6027<\/strong>\uff1a\u6570\u636e\u6837\u672c\u662f\u968f\u673a\u9009\u62e9\u7684\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u540c\u8d28\u6027<\/strong>\uff1a\u6570\u636e\u6837\u672c\u7684\u65b9\u5dee\u662f\u540c\u8d28\u7684\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u6b63\u6001\u6027<\/strong>\u2014\u2014\u5b9a\u4e49\u6570\u636e\u6837\u672c\u7684\u5206\u5e03\u8fd1\u4f3c\u6b63\u6001\u3002<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hacer-una-prueba-t-de-student\"><\/span>\u5982\u4f55\u8fdb\u884c\u5b66\u751f t \u68c0\u9a8c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u540e\uff0c\u603b\u800c\u8a00\u4e4b\uff0c\u8be6\u7ec6\u4ecb\u7ecd\u4e86\u6267\u884c\u5b66\u751f t \u68c0\u9a8c\u6240\u9700\u9075\u5faa\u7684\u6b65\u9aa4\u3002<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u5b9a\u4e49\u5047\u8bbe\u68c0\u9a8c\u7684<a href=\"https:\/\/statorials.org\/cn\/\u96f6\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\/\">\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe<\/a>\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u5efa\u7acb\u5047\u8bbe\u68c0\u9a8c\u7684<a href=\"https:\/\/statorials.org\/cn\/\u663e\u7740\u6027\u6c34\u5e73\/\">\u663e\u7740\u6027\u6c34\u5e73 (\u03b1)<\/a> \u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u9a8c\u8bc1\u5b66\u751f t \u68c0\u9a8c\u7684\u5047\u8bbe\u662f\u5426\u5f97\u5230\u6ee1\u8db3\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u5e94\u7528\u76f8\u5e94\u7684\u5b66\u751f t \u68c0\u9a8c\u516c\u5f0f\u5e76\u8ba1\u7b97\u68c0\u9a8c\u7edf\u8ba1\u91cf\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u901a\u8fc7\u5c06\u5b66\u751f t 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