{"id":271,"date":"2023-08-03T08:04:23","date_gmt":"2023-08-03T08:04:23","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%81%87%e8%ae%be%e5%af%b9%e6%af%94\/"},"modified":"2023-08-03T08:04:23","modified_gmt":"2023-08-03T08:04:23","slug":"%e5%81%87%e8%ae%be%e5%af%b9%e6%af%94","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%81%87%e8%ae%be%e5%af%b9%e6%af%94\/","title":{"rendered":"\u5047\u8bbe\u5bf9\u6bd4"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u5047\u8bbe\u68c0\u9a8c\u662f\u4ec0\u4e48\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u5b66\u4e60\u5982\u4f55\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\u3001\u4e0d\u540c\u7c7b\u578b\u7684\u5047\u8bbe\u68c0\u9a8c\u4ee5\u53ca\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\u65f6\u53ef\u80fd\u51fa\u73b0\u7684\u9519\u8bef\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-un-contraste-de-hipotesis\"><\/span>\u4ec0\u4e48\u662f\u5047\u8bbe\u68c0\u9a8c\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5047\u8bbe\u68c0\u9a8c<\/strong>\u662f\u7528\u4e8e\u62d2\u7edd\u6216\u5426\u5b9a\u7edf\u8ba1\u5047\u8bbe\u7684\u7a0b\u5e8f\u3002\u5728\u5047\u8bbe\u68c0\u9a8c\u4e2d\uff0c\u6211\u4eec\u5224\u65ad\u603b\u4f53\u53c2\u6570\u7684\u503c\u662f\u5426\u4e0e\u5728\u6240\u8ff0\u603b\u4f53\u6837\u672c\u4e2d\u89c2\u5bdf\u5230\u7684\u7ed3\u679c\u4e00\u81f4\u3002<\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u5047\u8bbe\u68c0\u9a8c\u4e2d\uff0c\u5bf9\u7edf\u8ba1\u6837\u672c\u8fdb\u884c\u5206\u6790\uff0c\u5e76\u6839\u636e\u83b7\u5f97\u7684\u7ed3\u679c\u786e\u5b9a\u662f\u62d2\u7edd\u8fd8\u662f\u63a5\u53d7\u5148\u524d\u5efa\u7acb\u7684\u5047\u8bbe\u3002<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u4e00\u822c\u6765\u8bf4\uff0c\u4ece\u5047\u8bbe\u68c0\u9a8c\u4e2d\uff0c\u4eba\u4eec\u65e0\u6cd5\u5b8c\u5168\u786e\u5b9a\u5730\u63a8\u65ad\u5047\u8bbe\u662f\u771f\u662f\u5047\uff0c\u4f46\u5047\u8bbe\u53ea\u662f\u88ab\u62d2\u7edd\u6216\u4e0d\u57fa\u4e8e\u6240\u83b7\u5f97\u7684\u7ed3\u679c\u3002\u56e0\u6b64\uff0c\u5728\u68c0\u9a8c\u5047\u8bbe\u65f6\uff0c\u5373\u4f7f\u6709\u7edf\u8ba1\u8bc1\u636e\u8868\u660e\u6240\u505a\u7684\u51b3\u5b9a\u662f\u6700\u6709\u53ef\u80fd\u7684\uff0c\u4ecd\u7136\u53ef\u80fd\u4f1a\u72af\u9519\u8bef\u3002<\/p>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u5047\u8bbe\u68c0\u9a8c\u4e5f\u79f0\u4e3a<strong>\u5047\u8bbe\u68c0\u9a8c<\/strong>\u3001<strong>\u5047\u8bbe\u68c0\u9a8c<\/strong>\u6216<strong>\u663e\u7740\u6027\u68c0\u9a8c<\/strong>\u3002<\/p>\n<p>\u5047\u8bbe\u68c0\u9a8c\u7406\u8bba\u7531\u82f1\u56fd\u7edf\u8ba1\u5b66\u5bb6\u7f57\u7eb3\u5fb7\u00b7\u8d39\u820d\u5c14 (Ronald Fisher) \u5efa\u7acb\uff0c\u5e76\u7531\u6770\u897f\u00b7\u5185\u66fc (Jerzy Neyman) \u548c\u57c3\u8d21\u00b7\u76ae\u5c14\u900a (Egon Pearson) \u8fdb\u4e00\u6b65\u53d1\u5c55\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"hipotesis-nula-e-hipotesis-alternativa\"><\/span>\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5047\u8bbe\u68c0\u9a8c\u7531\u4e24\u79cd\u7c7b\u578b\u7684\u7edf\u8ba1\u5047\u8bbe\u7ec4\u6210\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u96f6\u5047\u8bbe (H <sub>0<\/sub> )<\/strong> \uff1a\u8be5\u5047\u8bbe\u8ba4\u4e3a\u6211\u4eec\u5173\u4e8e\u603b\u4f53\u53c2\u6570\u7684\u521d\u59cb\u5047\u8bbe\u662f\u9519\u8bef\u7684\u3002\u56e0\u6b64\uff0c\u96f6\u5047\u8bbe\u662f\u6211\u4eec\u5e0c\u671b\u62d2\u7edd\u7684\u5047\u8bbe\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u5907\u62e9\u5047\u8bbe\uff08H <sub>1<\/sub> \uff09<\/strong> \uff1a\u662f\u5176\u771f\u5b9e\u6027\u5e94\u8be5\u88ab\u8bc1\u660e\u7684\u7814\u7a76\u5047\u8bbe\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5907\u62e9\u5047\u8bbe\u662f\u7814\u7a76\u8005\u7684\u5148\u9a8c\u5047\u8bbe\uff0c\u4e3a\u4e86\u8bd5\u56fe\u8bc1\u660e\u5176\u6b63\u786e\u6027\uff0c\u5c06\u8fdb\u884c\u5bf9\u6bd4\u5047\u8bbe\u3002<\/span><\/li>\n<\/ul>\n<p>\u5b9e\u9645\u4e0a\uff0c\u5907\u62e9\u5047\u8bbe\u662f\u5728\u539f\u5047\u8bbe\u4e4b\u524d\u5236\u5b9a\u7684\uff0c\u56e0\u4e3a\u5907\u62e9\u5047\u8bbe\u65e8\u5728\u901a\u8fc7\u6570\u636e\u6837\u672c\u7684\u7edf\u8ba1\u5206\u6790\u6765\u8bc1\u5b9e\u3002\u7136\u540e\u7b80\u5355\u5730\u901a\u8fc7\u53cd\u9a73\u5907\u62e9\u5047\u8bbe\u6765\u5236\u5b9a\u539f\u5047\u8bbe\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-contrastes-de-hipotesis\"><\/span>\u5047\u8bbe\u68c0\u9a8c\u7684\u7c7b\u578b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5047\u8bbe\u68c0\u9a8c\u53ef\u4ee5\u5206\u4e3a\u4e24\u79cd\u4e0d\u540c\u7684\u7c7b\u578b\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u53cc\u5c3e\u5047\u8bbe\u68c0\u9a8c\uff08\u6216\u53cc\u5c3e\u5047\u8bbe\u68c0\u9a8c\uff09<\/strong> \uff1a\u5047\u8bbe\u68c0\u9a8c\u7684\u5907\u62e9\u5047\u8bbe\u6307\u51fa\u603b\u4f53\u53c2\u6570\u4e0e\u7279\u5b9a\u503c\u201c\u4e0d\u540c\u201d\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u5355\u5c3e\u5047\u8bbe\u68c0\u9a8c\uff08\u6216\u5355\u5c3e\u5047\u8bbe\u68c0\u9a8c\uff09<\/strong> \uff1a\u5047\u8bbe\u68c0\u9a8c\u7684\u5907\u62e9\u5047\u8bbe\u8868\u660e\u603b\u4f53\u53c2\u6570\u201c\u5927\u4e8e\u201d\uff08\u53f3\u5c3e\uff09\u6216\u201c\u5c0f\u4e8e\u201d\uff08\u5de6\u5c3e\uff09\u67d0\u4e2a\u7279\u5b9a\u503c\u3002<\/span> <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-20 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#ff8a05\"><strong>\u53cc\u5c3e\u5047\u8bbe\u68c0\u9a8c<\/strong><\/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-4f0c1b65b50009900a6facbefea23ca1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu=\\mu_0\\\\[2ex]H_1:\\mu\\neq\\mu_0\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"102\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#ff8a05\"><strong>\u5355\u5c3e\u5047\u8bbe\u68c0\u9a8c\uff08\u53f3\u5c3e\uff09<\/strong> <\/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-1393df603c93485a0f75ebd0116c46a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu\\leq \\mu_0\\\\[2ex]H_1:\\mu>\\mu_0\\end{cases}&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;65&#8243; width=&#8221;102&#8243; style=&#8221;vertical-align: 0px;&#8221;><\/p>\n<\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<p class=\"has-text-align-center has-text-color\" style=\"color:#ff8a05\"><strong><strong>\u5355\u5c3e\u5047\u8bbe\u68c0\u9a8c\uff08\u5de6\u5c3e\uff09<\/strong><\/strong> <\/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-570fdfa44817f5392b33075476008f80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu\\geq\\mu_0\\\\[2ex]H_1:\\mu<\\mu_0\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"102\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"region-de-rechazo-y-region-de-aceptacion-de-un-contraste-de-hipotesis\"><\/span>\u5047\u8bbe\u68c0\u9a8c\u7684\u62d2\u7edd\u533a\u57df\u548c\u63a5\u53d7\u533a\u57df<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6b63\u5982\u6211\u4eec\u5c06\u5728\u4e0b\u9762\u8be6\u7ec6\u770b\u5230\u7684\uff0c\u5047\u8bbe\u68c0\u9a8c\u5305\u62ec\u8ba1\u7b97\u6bcf\u79cd\u5047\u8bbe\u68c0\u9a8c\u7684\u7279\u5f81\u503c\uff0c\u8be5\u503c\u79f0\u4e3a\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u3002\u56e0\u6b64\uff0c\u4e00\u65e6\u8ba1\u7b97\u51fa\u5bf9\u6bd4\u5ea6\u7edf\u8ba1\u91cf\uff0c\u5c31\u9700\u8981\u89c2\u5bdf\u5b83\u4f4d\u4e8e\u4ee5\u4e0b\u4e24\u4e2a\u533a\u57df\u4e2d\u7684\u54ea\u4e00\u4e2a\u533a\u57df\u624d\u80fd\u5f97\u51fa\u7ed3\u8bba\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:18px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u62d2\u7edd\u533a\u57df\uff08\u6216\u4e34\u754c\u533a\u57df\uff09<\/strong> \uff1a\u8fd9\u662f\u6d89\u53ca\u62d2\u7edd\u539f\u5047\u8bbe\uff08\u5e76\u63a5\u53d7\u5907\u62e9\u5047\u8bbe\uff09\u7684\u5047\u8bbe\u68c0\u9a8c\u53c2\u8003\u5206\u5e03\u7684\u56fe\u5f62\u533a\u57df\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u63a5\u53d7\u533a\u57df<\/strong>\uff1a\u8fd9\u662f\u5047\u8bbe\u68c0\u9a8c\u53c2\u8003\u5206\u5e03\u7684\u56fe\u5f62\u533a\u57df\uff0c\u610f\u5473\u7740\u63a5\u53d7\u539f\u5047\u8bbe\uff08\u5e76\u62d2\u7edd\u5907\u62e9\u5047\u8bbe\uff09\u3002<\/span><\/li>\n<\/ul>\n<p>\u7b80\u800c\u8a00\u4e4b\uff0c\u5982\u679c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u843d\u5728\u62d2\u7edd\u533a\u5185\uff0c\u5219\u62d2\u7edd\u539f\u5047\u8bbe\u5e76\u63a5\u53d7\u5907\u62e9\u5047\u8bbe\u3002\u76f8\u53cd\uff0c\u5982\u679c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u843d\u5728\u63a5\u53d7\u533a\u57df\u5185\uff0c\u5219\u63a5\u53d7\u539f\u5047\u8bbe\u5e76\u62d2\u7edd\u5907\u62e9\u5047\u8bbe\u3002 <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/test-dhypothese-de-contraste.png\" alt=\"\u5047\u8bbe\u5bf9\u6bd4\" class=\"wp-image-5660\" width=\"311\" height=\"600\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u5efa\u7acb\u62d2\u7edd\u533a\u57df\u548c\u63a5\u53d7\u533a\u57df\u8fb9\u754c\u7684\u503c\u79f0\u4e3a<strong>\u4e34\u754c\u503c<\/strong>\uff0c\u7c7b\u4f3c\u5730\uff0c\u5b9a\u4e49\u62d2\u7edd\u533a\u57df\u7684\u503c\u7684\u533a\u95f4\u79f0\u4e3a<strong>\u7f6e\u4fe1\u533a\u95f4<\/strong>\u3002\u8fd9\u4e24\u4e2a\u503c\u90fd\u53d6\u51b3\u4e8e\u6240\u9009\u7684<strong>\u663e\u7740\u6027\u6c34\u5e73<\/strong>\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\/\u663e\u7740\u6027\u6c34\u5e73\/\">Alpha \u663e\u7740\u6027\u7ea7\u522b<\/a><\/div>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u62d2\u7edd\u6216\u63a5\u53d7\u539f\u5047\u8bbe\u7684\u51b3\u5b9a\u4e5f\u53ef\u4ee5\u901a\u8fc7\u5c06\u4ece\u5047\u8bbe\u68c0\u9a8c\u83b7\u5f97\u7684<strong>p \u503c<\/strong>\uff08\u6216 p \u503c\uff09\u4e0e\u6240\u9009\u663e\u7740\u6027\u6c34\u5e73\u8fdb\u884c\u6bd4\u8f83\u6765\u505a\u51fa\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\/p\u503c\/\">p \u503c\u662f\u591a\u5c11\uff1f<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hacer-un-contraste-de-hipotesis\"><\/span>\u5982\u4f55\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u8981\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\uff0c\u5e94\u9075\u5faa\u4ee5\u4e0b\u6b65\u9aa4\uff1a<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u9648\u8ff0\u5047\u8bbe\u68c0\u9a8c\u7684\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5efa\u7acb\u6240\u9700\u7684 alpha (\u03b1) \u663e\u7740\u6027\u6c34\u5e73\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u8ba1\u7b97\u5047\u8bbe\u5bf9\u6bd4\u7edf\u8ba1\u91cf\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u786e\u5b9a\u5047\u8bbe\u68c0\u9a8c\u7684\u4e34\u754c\u503c\uff0c\u4ee5\u4e86\u89e3\u5047\u8bbe\u68c0\u9a8c\u7684\u62d2\u7edd\u57df\u548c\u63a5\u53d7\u57df\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u89c2\u5bdf\u5047\u8bbe\u5bf9\u6bd4\u7edf\u8ba1\u91cf\u662f\u5728\u62d2\u7edd\u533a\u57df\u8fd8\u662f\u63a5\u53d7\u533a\u57df\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u7edf\u8ba1\u91cf\u843d\u5728\u62d2\u7edd\u533a\u57df\u5185\uff0c\u5219\u62d2\u7edd\u539f\u5047\u8bbe\uff08\u5e76\u63a5\u53d7\u5907\u62e9\u5047\u8bbe\uff09\u3002\u4f46\u5982\u679c\u7edf\u8ba1\u91cf\u843d\u5728\u63a5\u53d7\u533a\u5185\uff0c\u5219\u63a5\u53d7\u539f\u5047\u8bbe\uff08\u5e76\u62d2\u7edd\u5907\u62e9\u5047\u8bbe\uff09\u3002<\/span> <\/li>\n<\/ol>\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\u7684\u5047\u8bbe\u68c0\u9a8c<\/a><br \/><span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c\/\">\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c<\/a><br \/><span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u65b9\u5dee\u5047\u8bbe\u68c0\u9a8c\/\">\u65b9\u5dee\u5047\u8bbe\u68c0\u9a8c<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"errores-de-un-contraste-de-hipotesis\"><\/span>\u5047\u8bbe\u68c0\u9a8c\u9519\u8bef<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728\u5047\u8bbe\u68c0\u9a8c\u4e2d\uff0c\u5f53\u62d2\u7edd\u4e00\u4e2a\u5047\u8bbe\u5e76\u63a5\u53d7\u53e6\u4e00\u4e2a\u68c0\u9a8c\u5047\u8bbe\u65f6\uff0c\u53ef\u80fd\u4f1a\u72af\u4ee5\u4e0b\u4e24\u4e2a\u9519\u8bef\u4e4b\u4e00\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>I \u7c7b\u9519\u8bef<\/strong>\uff1a\u8fd9\u662f\u5728\u539f\u5047\u8bbe\u4e3a\u771f\u65f6\u62d2\u7edd\u539f\u5047\u8bbe\u65f6\u6240\u72af\u7684\u9519\u8bef\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>II \u7c7b\u9519\u8bef<\/strong>\uff1a\u8fd9\u662f\u5728\u539f\u5047\u8bbe\u5b9e\u9645\u4e0a\u4e3a\u5047\u65f6\u63a5\u53d7\u539f\u5047\u8bbe\u800c\u72af\u7684\u9519\u8bef\u3002<\/span> <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/erreur-type-i-et-erreur-type-ii.png\" alt=\"I \u7c7b\u9519\u8bef\u548c II \u7c7b\u9519\u8bef\" class=\"wp-image-5683\" width=\"456\" height=\"120\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u72af\u6bcf\u79cd\u7c7b\u578b\u9519\u8bef\u7684\u6982\u7387\u5982\u4e0b\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Alpha\u6982\u7387\uff08\u03b1\uff09<\/strong> \uff1a\u662f\u72af\u7b2c\u4e00\u7c7b\u9519\u8bef\u7684\u6982\u7387\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Beta\u6982\u7387\uff08\u03b2\uff09<\/strong> \uff1a\u662f\u72af\u7b2c\u4e8c\u7c7b\u9519\u8bef\u7684\u6982\u7387\u3002<\/span><\/li>\n<\/ul>\n<p>\u7c7b\u4f3c\u5730\uff0c<strong>\u5047\u8bbe\u68c0\u9a8c\u7684\u529f\u6548<\/strong>\u88ab\u5b9a\u4e49\u4e3a\u5f53\u539f\u5047\u8bbe\uff08H <sub>0<\/sub> \uff09\u4e3a\u5047\u65f6\u62d2\u7edd\u539f\u5047\u8bbe\uff08H 0 \uff09\u7684\u6982\u7387\uff0c\u6216\u8005\u6362\u53e5\u8bdd\u8bf4\uff0c\u5b83\u662f\u5f53\u5907\u62e9\u5047\u8bbe\uff08H <sub>1<\/sub> \uff09\u4e3a\u771f\u65f6\u9009\u62e9\u5b83\u7684\u6982\u7387\u3002\u56e0\u6b64\uff0c\u5047\u8bbe\u68c0\u9a8c\u7684\u529f\u6548\u7b49\u4e8e 1-\u03b2\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"estadisticos-de-contrastes-de-hipotesis\"><\/span>\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5047\u8bbe\u68c0\u9a8c\u7684\u7edf\u8ba1\u91cf<\/strong>\u662f\u5047\u8bbe\u68c0\u9a8c\u53c2\u8003\u5206\u5e03\u7684\u503c\uff0c\u7528\u4e8e\u786e\u5b9a\u662f\u5426\u62d2\u7edd\u539f\u5047\u8bbe\u3002\u5982\u679c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u843d\u5165\u62d2\u7edd\u57df\uff0c\u5219\u62d2\u7edd\u539f\u5047\u8bbe\uff08\u5e76\u63a5\u53d7\u5907\u62e9\u5047\u8bbe\uff09\uff0c\u53cd\u4e4b\uff0c\u5982\u679c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u843d\u5165\u63a5\u53d7\u57df\uff0c\u5219\u63a5\u53d7\u539f\u5047\u8bbe\uff08\u5e76\u63a5\u53d7\u5907\u62e9\u5047\u8bbe\uff09\u62d2\u7edd\uff09\u3002\u66ff\u4ee3\u5047\u8bbe\uff09\u3002<\/p>\n<p>\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u8ba1\u7b97\u53d6\u51b3\u4e8e\u68c0\u9a8c\u7684\u7c7b\u578b\u3002\u56e0\u6b64\uff0c\u6bcf\u79cd\u5047\u8bbe\u68c0\u9a8c\u7684\u7edf\u8ba1\u91cf\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0b\u6240\u793a\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"contraste-de-hipotesis-para-la-media\"><\/span>\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u5df2\u77e5\u65b9\u5dee\u7684\u5747\u503c\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-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\">\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\u5e73\u5747\u503c\u7684\u5047\u8bbe\u5bf9\u6bd4\u7edf\u8ba1\u91cf\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\u5efa\u8bae\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-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>\u662f\u603b\u4f53\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\u5e73\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u540e\uff0c\u5fc5\u987b\u89e3\u91ca\u7ed3\u679c\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\u5219\u5f53\u7edf\u8ba1\u91cf\u7684\u7edd\u5bf9\u503c\u5927\u4e8e\u4e34\u754c\u503c Z <sub>\u03b1\/2<\/sub>\u65f6\uff0c\u5c06\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\u4e14\u7edf\u8ba1\u91cf\u5927\u4e8e\u4e34\u754c\u503c Z <sub>\u03b1<\/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\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\u4e0e\u5de6\u5c3e\u5339\u914d\uff0c\u4e14\u7edf\u8ba1\u91cf\u5c0f\u4e8e\u4e34\u754c\u503c -Z <sub>\u03b1<\/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-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>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4e34\u754c\u503c\u662f\u4ece\u6807\u51c6\u5316\u6b63\u6001\u5206\u5e03\u8868\u4e2d\u83b7\u5f97\u7684\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c<strong>\u65b9\u5dee\u672a\u77e5\u7684\u5747\u503c\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-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\u5efa\u8bae\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>\u548c\u4ee5\u524d\u4e00\u6837\uff0c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u8ba1\u7b97\u7ed3\u679c\u5fc5\u987b\u7528\u4e34\u754c\u503c\u6765\u89e3\u91ca\uff0c\u4ee5\u62d2\u7edd\u6216\u4e0d\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\u7edf\u8ba1\u91cf\u7684\u7edd\u5bf9\u503c\u5927\u4e8e\u4e34\u754c\u503c t <sub>\u03b1\/2|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\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\u4e0e\u53f3\u5c3e\u5339\u914d\uff0c\u4e14\u7edf\u8ba1\u91cf\u5927\u4e8e\u4e34\u754c\u503c t <sub>\u03b1|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\u5de6\u5c3e\u5339\u914d\uff0c\u4e14\u7edf\u8ba1\u91cf\u5c0f\u4e8e\u4e34\u754c\u503c -t <sub>\u03b1|n-1 \uff0c<\/sub>\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>\u5f53\u65b9\u5dee\u672a\u77e5\u65f6\uff0c\u4eceStudent\u5206\u5e03\u8868\u4e2d\u83b7\u5f97\u4e34\u754c\u6d4b\u8bd5\u503c\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"contraste-de-hipotesis-para-la-proporcion\"><\/span>\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u6bd4\u4f8b\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-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\">\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\u8be5\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\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-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>\u662f\u6837\u672c\u6bd4\u4f8b\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-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>\u662f\u5efa\u8bae\u7684\u6bd4\u4f8b\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-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<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>\u662f\u6bd4\u4f8b\u7684\u6807\u51c6\u5dee\u3002<\/li>\n<\/ul>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u8ba1\u7b97\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u662f\u4e0d\u591f\u7684\uff0c\u4f46\u5fc5\u987b\u89e3\u91ca\u7ed3\u679c\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\u8be5\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u662f\u53cc\u5411\u7684\uff0c\u5219\u5f53\u7edf\u8ba1\u91cf\u7684\u7edd\u5bf9\u503c\u5927\u4e8e\u4e34\u754c\u503c Z <sub>\u03b1\/2<\/sub>\u65f6\uff0c\u5c06\u62d2\u7edd\u539f\u5047\u8bbe\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u8be5\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u4e0e\u53f3\u5c3e\u5339\u914d\uff0c\u4e14\u7edf\u8ba1\u91cf\u5927\u4e8e\u4e34\u754c\u503c Z <sub>\u03b1<\/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\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u4e0e\u5de6\u5c3e\u5339\u914d\uff0c\u4e14\u7edf\u8ba1\u91cf\u5c0f\u4e8e\u4e34\u754c\u503c -Z <sub>\u03b1<\/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-7d5bd583532769e3014286e8ffd94c9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: p\\neq p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |Z|>Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: p> p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: p< p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z<-Z_{\\alpha} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"437\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u8bf7\u8bb0\u4f4f\uff0c\u53ef\u4ee5\u4ece\u6807\u51c6\u6b63\u6001\u5206\u5e03\u8868\u4e2d\u8f7b\u677e\u83b7\u5f97\u4e34\u754c\u503c\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"contraste-de-hipotesis-para-la-varianza\"><\/span>\u65b9\u5dee\u5047\u8bbe\u68c0\u9a8c<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u65b9\u5dee\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u8ba1\u7b97\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-3917636d4c911eeaad1a005195204d08_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2=\\cfrac{(n-1)s^2}{\\sigma^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"115\" style=\"vertical-align: -12px;\"><\/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-984dc78529fc235b078a9f3b62d0f0c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u65b9\u5dee\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\uff0c\u5177\u6709\u5361\u65b9\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-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<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3ab572e85f9cb7cb6f495387f2a6ab0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u6837\u672c\u65b9\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-c6d52162ef1ec2e8130fb00687aca707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma^2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u5efa\u8bae\u603b\u4f53\u7684\u65b9\u5dee\u3002<\/li>\n<\/ul>\n<p>\u4e3a\u4e86\u89e3\u91ca\u7edf\u8ba1\u7ed3\u679c\uff0c\u5fc5\u987b\u5c06\u83b7\u5f97\u7684\u503c\u4e0e\u6d4b\u8bd5\u7684\u4e34\u754c\u503c\u8fdb\u884c\u6bd4\u8f83\u3002<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u65b9\u5dee\u5047\u8bbe\u68c0\u9a8c\u662f\u53cc\u5c3e\u7684\uff0c\u5219\u5f53\u7edf\u8ba1\u91cf\u5927\u4e8e\u4e34\u754c\u503c\u65f6\uff0c\u5c06\u62d2\u7edd\u539f\u5047\u8bbe\u3002\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7bd4ac2951fb286bf19797944cba6955_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{1-\\alpha\/2|n-1}^2\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"81\" style=\"vertical-align: -10px;\"><\/p>\n<p><\/span>\u6216\u8005\u5982\u679c\u4e34\u754c\u503c\u5c0f\u4e8e<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-931a3f10ab51df1c9003e6cb593907c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{\\alpha\/2|n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"63\" style=\"vertical-align: -8px;\"><\/p>\n<p>\u3002<\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u65b9\u5dee\u7684\u5047\u8bbe\u68c0\u9a8c\u4e0e\u53f3\u5c3e\u5339\u914d\uff0c\u4e14\u7edf\u8ba1\u91cf\u5927\u4e8e\u4e34\u754c\u503c\uff0c\u5219\u62d2\u7edd\u539f\u5047\u8bbe\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-243ef3cc114070613fd8bee8c61f8c13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{1-\\alpha|n-1}^2\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"67\" style=\"vertical-align: -10px;\"><\/p>\n<p><\/span>\u3002<\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5982\u679c\u65b9\u5dee\u5047\u8bbe\u68c0\u9a8c\u4e0e\u5de6\u5c3e\u5339\u914d\uff0c\u4e14\u7edf\u8ba1\u91cf\u5c0f\u4e8e\u4e34\u754c\u503c\uff0c\u5219\u62d2\u7edd\u539f\u5047\u8bbe\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0436c61e0bdff7a21f6e6ab296607c66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\chi_{\\alpha|n-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -8px;\"><\/p>\n<p><\/span>\u3002<\/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-ca46378c1a2ee04b5cc5bfa93002fe9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: \\sigma^2\\neq \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } \\chi^2>\\chi^2_{1-\\alpha\/2|n-1}\\text{ se rechaza } H_0\\\\[3ex]H_1: \\sigma^2\\neq \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si }\\chi^2<\\chi^2_{\\alpha\/2|n-1}\\text{ se rechaza } H_0 \\\\[3ex]H_1: \\sigma^2> \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } \\chi^2>\\chi^2_{1-\\alpha|n-1}\\text{ se rechaza } H_0\\\\[3ex]H_1: \\sigma^2< \\sigma_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } \\chi^2<\\chi^2_{\\alpha|n-1}\\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"160\" width=\"489\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u65b9\u5dee\u7684\u4e34\u754c\u5047\u8bbe\u68c0\u9a8c\u503c\u662f\u4ece\u5361\u65b9\u5206\u5e03\u8868\u4e2d\u83b7\u5f97\u7684\u3002\u8bf7\u6ce8\u610f\uff0c\u5361\u65b9\u5206\u5e03\u7684\u81ea\u7531\u5ea6\u662f\u6837\u672c\u5927\u5c0f\u51cf 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