{"id":285,"date":"2023-08-03T03:11:14","date_gmt":"2023-08-03T03:11:14","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%9d%87%e5%80%bc%e5%b7%ae%e5%bc%82%e7%9a%84%e5%81%87%e8%ae%be%e6%a3%80%e9%aa%8c\/"},"modified":"2023-08-03T03:11:14","modified_gmt":"2023-08-03T03:11:14","slug":"%e5%9d%87%e5%80%bc%e5%b7%ae%e5%bc%82%e7%9a%84%e5%81%87%e8%ae%be%e6%a3%80%e9%aa%8c","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%9d%87%e5%80%bc%e5%b7%ae%e5%bc%82%e7%9a%84%e5%81%87%e8%ae%be%e6%a3%80%e9%aa%8c\/","title":{"rendered":"\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u5747\u503c\u5dee\u5f02\u5047\u8bbe\u68c0\u9a8c\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u540c\u6837\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u5bf9\u5747\u503c\u5dee\u5f02\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\u4ee5\u53ca\u9010\u6b65\u89e3\u51b3\u7684\u7ec3\u4e60\u3002 <\/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>\u4ec0\u4e48\u662f\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c<\/strong>\u662f\u4e00\u79cd\u7edf\u8ba1\u68c0\u9a8c\uff0c\u7528\u4e8e\u62d2\u7edd\u6216\u63a5\u53d7\u4e24\u4e2a\u603b\u4f53\u7684\u5747\u503c\u4e0d\u540c\u7684\u5047\u8bbe\u3002\u5373\u5747\u503c\u5dee\u5f02\u5047\u8bbe\u68c0\u9a8c\u7528\u4e8e\u786e\u5b9a\u4e24\u4e2a\u603b\u4f53\u7684\u5747\u503c\u662f\u5426\u76f8\u540c\u6216\u4e0d\u540c\u3002<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u5047\u8bbe\u68c0\u9a8c\u4e2d\u505a\u51fa\u7684\u51b3\u7b56\u662f\u57fa\u4e8e\u5148\u524d\u5efa\u7acb\u7684<a href=\"https:\/\/statorials.org\/cn\/\u4e00\u5b9a\u7a0b\u5ea6\u7684\u4fe1\u5fc3\/\">\u7f6e\u4fe1\u6c34\u5e73<\/a>\uff0c\u56e0\u6b64\u4e0d\u80fd\u4fdd\u8bc1\u5047\u8bbe\u68c0\u9a8c\u7684\u7ed3\u679c\u59cb\u7ec8\u6b63\u786e\uff0c\u800c\u662f\u4fdd\u8bc1\u5b83\u662f\u6700\u6709\u53ef\u80fd\u4e3a\u771f\u7684\u7ed3\u679c\u3002<\/p>\n<p>\u5bf9\u4e24\u4e2a\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c\u6d89\u53ca\u8ba1\u7b97\u68c0\u9a8c\u7edf\u8ba1\u91cf\u5e76\u5c06\u5176\u4e0e\u4e34\u754c\u503c\u8fdb\u884c\u6bd4\u8f83\u4ee5\u62d2\u7edd\u96f6\u5047\u8bbe\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u4e86\u89e3\u5982\u4f55\u5bf9\u5747\u503c\u5dee\u5f02\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\u3002<\/p>\n<p>\u6700\u540e\uff0c\u8bf7\u8bb0\u4f4f\uff0c\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u5047\u8bbe\u68c0\u9a8c\u4e5f\u53ef\u4ee5\u79f0\u4e3a\u5047\u8bbe\u5bf9\u6bd4\u3001\u5047\u8bbe\u68c0\u9a8c\u6216\u663e\u7740\u6027\u68c0\u9a8c\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\/\u5747\u503c\u5dee\u7684\u62bd\u6837\u5206\u5e03\/\">\u5747\u503c\u5dee\u5f02\u7684\u62bd\u6837\u5206\u5e03<\/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>\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7528\u4e8e\u68c0\u9a8c\u5747\u503c\u5dee\u5f02\u5047\u8bbe\u7684\u516c\u5f0f\u4f1a\u6709\u6240\u4e0d\u540c\uff0c\u5177\u4f53\u53d6\u51b3\u4e8e\u603b\u4f53\u65b9\u5dee\u662f\u5426\u5df2\u77e5\uff0c\u5982\u679c\u672a\u77e5\uff0c\u5219\u662f\u5426\u53ef\u4ee5\u5047\u8bbe\u5b83\u4eec\u76f8\u540c\u6216\u4e0d\u540c\u3002\u56e0\u6b64\uff0c\u5728\u672c\u8282\u4e2d\uff0c\u6211\u4eec\u5c06\u6839\u636e\u60c5\u51b5\u4e86\u89e3\u4f7f\u7528\u54ea\u4e2a\u516c\u5f0f\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-conocidas\"><\/span>\u5df2\u77e5\u7684\u53d8\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u5f53\u65b9\u5dee\u5df2\u77e5\u65f6\uff0c\u8ba1\u7b97\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\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-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\">\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-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>\u662f\u5df2\u77e5\u65b9\u5dee\u7684\u4e24\u4e2a\u5747\u503c\u4e4b\u5dee\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u9075\u5faa\u6807\u51c6\u6b63\u6001\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>\u8bf7\u8bb0\u4f4f\uff0c\u8fd9\u662f\u6700\u4e0d\u5e38\u89c1\u7684\u60c5\u51b5\uff0c\u56e0\u6b64\u8be5\u516c\u5f0f\u4ec5\u5728\u67d0\u4e9b\u7279\u5b9a\u60c5\u51b5\u4e0b\u4f7f\u7528\u3002<\/p>\n<h3 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><\/h3>\n<p><strong>\u5f53\u603b\u4f53\u65b9\u5dee\u672a\u77e5\u4f46\u5047\u8bbe\u76f8\u7b49\u65f6\uff0c\u8ba1\u7b97\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\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-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\u5f02\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\u7ec4\u5408\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>\u4e24\u4e2a\u6837\u672c\u7684\u7ec4\u5408\u6807\u51c6\u5dee\u6309\u4e0b\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-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>\u672a\u77e5\u548c\u4e0d\u540c\u7684\u53d8\u5316<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u5f53\u603b\u4f53\u65b9\u5dee\u672a\u77e5\u5e76\u4e14\u5047\u8bbe\u5b83\u4eec\u4e0d\u540c\u65f6\uff0c\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b<\/strong>\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\u5f02\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\u7f6e\u4fe1\u533a\u95f4\/\">\u5747\u503c\u5dee\u7684\u7f6e\u4fe1\u533a\u95f4\u516c\u5f0f<\/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>\u5747\u503c\u5dee\u5f02\u5047\u8bbe\u68c0\u9a8c\u7684\u5177\u4f53\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u5b8c\u6210\u5bf9\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c\u6982\u5ff5\u7684\u7406\u89e3\uff0c\u6211\u4eec\u5c06\u770b\u5230\u6b64\u7c7b\u5047\u8bbe\u68c0\u9a8c\u7684\u5177\u4f53\u793a\u4f8b\u3002<\/p>\n<ul>\n<li>\u60a8\u60f3\u8981\u5bf9\u4e24\u5bb6\u7ade\u4e89\u516c\u53f8\u7684\u85aa\u8d44\u8fdb\u884c\u7edf\u8ba1\u7814\u7a76\uff0c\u66f4\u5177\u4f53\u5730\u8bf4\uff0c\u60a8\u60f3\u8981\u786e\u5b9a\u4e24\u5bb6\u516c\u53f8\u7684\u5e73\u5747\u85aa\u8d44\u662f\u5426\u4e0d\u540c\u3002\u4e3a\u6b64\uff0c\u6211\u4eec\u62bd\u53d6\u4e86\u4e00\u5bb6\u516c\u53f8\u7684 47 \u540d\u5de5\u4eba\u6837\u672c\u548c\u53e6\u4e00\u5bb6\u516c\u53f8\u7684 55 \u540d\u5de5\u4eba\u6837\u672c\u3002\u4ece\u7b2c\u4e00\u4e2a\u6837\u672c\u4e2d\u83b7\u5f97\u7684\u5e73\u5747\u5de5\u8d44\u4e3a 40,000 \u7f8e\u5143\uff0c\u6807\u51c6\u5dee\u4e3a 12,000 \u7f8e\u5143\uff0c\u800c\u4ece\u7b2c\u4e8c\u4e2a\u6837\u672c\u4e2d\u83b7\u5f97\u7684\u5e73\u5747\u5de5\u8d44\u4e3a 46,000 \u7f8e\u5143\uff0c\u6807\u51c6\u5dee\u4e3a 18,000 \u7f8e\u5143\u3002\u6267\u884c 5% \u663e\u7740\u6027\u6c34\u5e73\u7684\u5047\u8bbe\u68c0\u9a8c\uff0c\u4ee5\u786e\u5b9a\u5e73\u5747\u5de5\u8d44\u662f\u5426\u4e0d\u540c\u3002<\/li>\n<\/ul>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e24\u4e2a\u5747\u503c\u5dee\u5f02\u7684\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<\/a>\u5047\u8bbe\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-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>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4eba\u53e3\u5dee\u8ddd\u662f\u672a\u77e5\u7684\uff0c\u4f46\u53ef\u4ee5\u5047\u8bbe\u5b83\u4eec\u662f\u76f8\u7b49\u7684\uff0c\u56e0\u4e3a\u5b83\u4eec\u662f\u7ade\u4e89\u516c\u53f8\uff0c\u5e76\u4e14\u5b83\u4eec\u6240\u7ecf\u8425\u7684\u5e02\u573a\u7684\u5de5\u4f5c\u6761\u4ef6\u975e\u5e38\u76f8\u4f3c\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u5e94\u8be5\u4f7f\u7528\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u516c\u5f0f\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-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>\u56e0\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\u4e24\u4e2a\u6837\u672c\u7684\u5408\u5e76\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-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>\u6211\u4eec\u73b0\u5728\u5e94\u7528\u5047\u8bbe\u68c0\u9a8c\u516c\u5f0f\u6765\u8ba1\u7b97\u5747\u503c\u5dee\u5f02\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-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>\u53e6\u4e00\u65b9\u9762\uff0c\u6211\u4eec\u5728<a href=\"https:\/\/statorials.org\/cn\/\u5b66\u751ft\u5206\u5e03\u8868\/\">Student t \u8868<\/a>\u4e2d\u5bfb\u627e\u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c\u7684\u4e34\u754c\u503c\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-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>\u7136\u540e\uff0c\u7531\u4e8e\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u7edd\u5bf9\u503c\u5c0f\u4e8e\u4e34\u754c\u68c0\u9a8c\u503c\uff0c\u56e0\u6b64\u63a5\u53d7\u539f\u5047\u8bbe\u5e76\u62d2\u7edd\u5907\u62e9\u5047\u8bbe\u3002<\/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>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u5747\u503c\u5dee\u5f02\u5047\u8bbe\u68c0\u9a8c\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u540c\u6837\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u5bf9\u5747\u503c\u5dee\u5f02\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\u4ee5\u53ca\u9010\u6b65\u89e3\u51b3\u7684 [&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-285","post","type-post","status-publish","format-standard","hentry","category-14"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u5747\u503c\u5dee\u5f02\u7684\u5047\u8bbe\u68c0\u9a8c<\/title>\n<meta name=\"description\" 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