{"id":270,"date":"2023-08-03T08:29:13","date_gmt":"2023-08-03T08:29:13","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%a0%b7%e6%9c%ac%e6%af%94%e4%be%8b\/"},"modified":"2023-08-03T08:29:13","modified_gmt":"2023-08-03T08:29:13","slug":"%e6%a0%b7%e6%9c%ac%e6%af%94%e4%be%8b","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%a0%b7%e6%9c%ac%e6%af%94%e4%be%8b\/","title":{"rendered":"\u6837\u672c\u6bd4\u4f8b"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u7edf\u8ba1\u5b66\u4e2d\u7684\u6837\u672c\u6bd4\u4f8b\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u6837\u672c\u6bd4\u4f8b\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\uff0c\u4ee5\u53ca\u6837\u672c\u6bd4\u4f8b\u548c\u603b\u4f53\u6bd4\u4f8b\u4e4b\u95f4\u7684\u5dee\u5f02\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-proporcion-muestral\"><\/span>\u6837\u672c\u6bd4\u4f8b\u662f\u591a\u5c11\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6837\u672c\u6bd4\u4f8b<\/strong>\u662f\u6837\u672c\u4e2d\u6210\u529f\u6848\u4f8b\u4e0e\u6837\u672c\u91cf\u7684\u6bd4\u7387\u3002\u56e0\u6b64\uff0c\u8981\u8ba1\u7b97\u6837\u672c\u6bd4\u4f8b\uff0c\u5fc5\u987b\u5c06\u6837\u672c\u4e2d\u6210\u529f\u7684\u6570\u91cf\u9664\u4ee5\u6570\u636e\u603b\u6570\u3002<\/p>\n<p>\u6837\u672c\u6bd4\u4f8b\u7684\u7b26\u53f7\u4e3a<\/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-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>\u3002<\/p>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u8fdb\u884c\u8c03\u67e5\u65f6\uff0c\u901a\u5e38\u5e76\u4e0d\u77e5\u9053\u6240\u6709\u603b\u4f53\u6570\u636e\uff0c\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u901a\u5e38\u5bf9\u4ee3\u8868\u6027\u6837\u672c\u8fdb\u884c\u7814\u7a76\uff0c\u7136\u540e\u5c06\u5f97\u51fa\u7684\u7ed3\u8bba\u5916\u63a8\u5230\u6574\u4e2a\u603b\u4f53\u3002\u4eba\u53e3\u3002\u56e0\u6b64\uff0c\u6837\u672c\u6bd4\u4f8b\u7528\u4e8e\u4f30\u8ba1\u6574\u4e2a\u603b\u4f53\u7684\u6bd4\u4f8b\u3002\u4e0b\u9762\u6211\u4eec\u5c06\u770b\u5230\u8fd9\u662f\u5982\u4f55\u5b8c\u6210\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\/\u4ee3\u8868\u6027\u6837\u672c1\/\">\u4ec0\u4e48\u662f\u4ee3\u8868\u6027\u6837\u672c\uff1f<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-proporcion-muestral\"><\/span>\u6bd4\u4f8b\u516c\u5f0f\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6837\u672c\u6bd4\u4f8b\u7b49\u4e8e\u6837\u672c\u4e2d\u6210\u529f\u6848\u4f8b\u7684\u6570\u91cf\u9664\u4ee5\u6837\u672c\u91cf\u3002\u56e0\u6b64\uff0c<strong>\u6837\u672c\u6bd4\u4f8b\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-8497d73f09738f45701a70350badaacd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}=\\cfrac{e}{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"46\" 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 style=\"margin-bottom:3px\">\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 style=\"margin-bottom:3px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-558a73dc6903ad0c33580b0ce9f110d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u6837\u672c\u4e2d\u6210\u529f\u6848\u4f8b\u7684\u6570\u91cf\u3002<\/li>\n<li style=\"margin-bottom:3px\">\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\u4e2d\u6570\u636e\u9879\u7684\u603b\u6570\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-la-proporcion-muestral\"><\/span>\u6837\u54c1\u6bd4\u4f8b\u8ba1\u7b97\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e86\u89e3\u4e86\u6837\u672c\u6bd4\u4f8b\u7684\u5b9a\u4e49\u53ca\u5176\u516c\u5f0f\u662f\u4ec0\u4e48\u540e\uff0c\u672c\u8282\u6211\u4eec\u5c06\u89e3\u51b3\u4e00\u4e2a\u7b80\u5355\u7684\u793a\u4f8b\uff0c\u4ee5\u4fbf\u60a8\u4e86\u89e3\u6837\u672c\u6bd4\u4f8b\u662f\u5982\u4f55\u8ba1\u7b97\u7684\u3002<\/p>\n<ul>\n<li>\u4e00\u5bb6\u516c\u53f8\u751f\u4ea7\u4e00\u79cd\u73a9\u5177\uff0c\u5e76\u4ece\u53e6\u4e00\u5bb6\u5916\u90e8\u516c\u53f8\u8d2d\u4e70\u5176\u4e2d\u4e00\u4e2a\u96f6\u4ef6\u3002\u7136\u800c\uff0c\u5728\u4ed6\u8d2d\u4e70\u7684\u6279\u6b21\u4e2d\uff0c\u51fa\u73b0\u4e86\u7f3a\u9677\u96f6\u4ef6\uff0c\u56e0\u6b64\u4ed6\u51b3\u5b9a\u8fdb\u884c\u7edf\u8ba1\u7814\u7a76\uff0c\u627e\u51fa\u5b8c\u597d\u96f6\u4ef6\u7684\u6bd4\u4f8b\u548c\u7f3a\u9677\u96f6\u4ef6\u7684\u6bd4\u4f8b\u3002\u56e0\u6b64\uff0c\u60a8\u8ba2\u8d2d\u4e86 1,000 \u4e2a\u5355\u4f4d\u7684\u6837\u54c1\uff0c\u5e76\u53d1\u73b0\u4e86 138 \u4e2a\u6709\u7f3a\u9677\u7684\u96f6\u4ef6\u3002\u6837\u672c\u4e2d\u72b6\u51b5\u826f\u597d\u7684\u96f6\u4ef6\u6240\u5360\u7684\u6bd4\u4f8b\u662f\u591a\u5c11\uff1f\u6837\u54c1\u4e2d\u7f3a\u9677\u96f6\u4ef6\u7684\u6bd4\u4f8b\u662f\u591a\u5c11\uff1f<\/li>\n<\/ul>\n<p>\u6837\u672c\u4e2d\u672a\u635f\u574f\u96f6\u4ef6\u7684\u6570\u91cf\u4e3a 1000 \u51cf\u53bb\u6709\u7f3a\u9677\u96f6\u4ef6\u7684\u6570\u91cf\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-eba1cfb3b37e9124aa6a8f3d61ba3023_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e=1000-138=862\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"165\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4e3a\u4e86\u627e\u5230\u6837\u672c\u6bd4\u4f8b\uff0c\u6211\u4eec\u5e94\u7528\u4e0a\u9762\u770b\u5230\u7684\u516c\u5f0f\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-becf48230461723d7a4d320217ad95fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}=\\cfrac{e}{n}=\\cfrac{862}{1000}=0,862\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"174\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u90e8\u4ef6\u72b6\u51b5\u826f\u597d\u7684\u6837\u672c\u6bd4\u4f8b\u4e3a 86.2%\u3002<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u7f3a\u9677\u96f6\u4ef6\u7684\u6bd4\u4f8b\u7b49\u4e8e\u4e00\u51cf\u53bb\u5408\u683c\u96f6\u4ef6\u7684\u6bd4\u4f8b\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-14b45b7c5bc9fb8770efa40fac1f9e45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{q}=1-\\widehat{p}=1-0,862=0,138\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"237\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u7f3a\u9677\u96f6\u4ef6\u7684\u6837\u672c\u6bd4\u4f8b\u4e3a 13.8%\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"proporcion-muestral-y-proporcion-poblacional\"><\/span>\u6837\u672c\u6bd4\u4f8b\u548c\u603b\u4f53\u6bd4\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4eba\u53e3\u6bd4\u91cd<\/strong>\u662f\u6307\u7edf\u8ba1\u4eba\u53e3\u6240\u5360\u7684\u6bd4\u4f8b\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u603b\u4f53\u6bd4\u4f8b\u662f\u6240\u7814\u7a76\u7684\u603b\u4f53\u7684\u6210\u529f\u6848\u4f8b\u4e0e\u5c5e\u4e8e\u8be5\u603b\u4f53\u7684\u6240\u6709\u5143\u7d20\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u5168\u56fd\u6bd4\u4f8b\u4e0e\u4eba\u53e3\u6bd4\u4f8b\u7684\u533a\u522b<\/strong>\u5728\u4e8e\uff0c\u5168\u56fd\u6bd4\u4f8b\u662f\u5360\u591a\u6570\u7684\u4e8b\u4ef6\u7684\u6bd4\u4f8b\uff0c\u800c\u4eba\u53e3\u6bd4\u4f8b\u5219\u662f\u6307\u6d89\u53ca\u6240\u6709\u8981\u7d20\u4eba\u53e3\u7684\u4e8b\u4ef6\u7684\u6bd4\u4f8b\u3002<\/p>\n<p>\u4e3a\u4e86\u533a\u5206\u6837\u672c\u6bd4\u4f8b\u548c\u603b\u4f53\u6bd4\u4f8b\uff0c\u5b83\u4eec\u7528\u4e0d\u540c\u7684\u7b26\u53f7\u8868\u793a\u3002\u6837\u672c\u6bd4\u4f8b\u7684\u7b26\u53f7\u4e3a<\/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-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>\uff0c\u800c\u4eba\u53e3\u6bd4\u4f8b\u7684\u7b26\u53f7\u662f<\/p>\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>\u3002<\/p>\n<p>\u4e00\u822c\u6765\u8bf4\uff0c\u4eba\u53e3\u6bd4\u4f8b\u65e0\u6cd5\u7cbe\u786e\u786e\u5b9a\uff0c\u56e0\u4e3a\u901a\u5e38\u5e76\u975e\u6240\u6709\u4eba\u53e3\u503c\u90fd\u662f\u5df2\u77e5\u7684\u3002\u76f8\u53cd\uff0c\u901a\u5e38\u4f7f\u7528\u5177\u6709\u4ee5\u4e0b\u516c\u5f0f\u7684\u7f6e\u4fe1\u533a\u95f4\u6765\u4f30\u8ba1\u603b\u4f53\u6bd4\u4f8b\u7684\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-6517d510181870c58b167c4d9712a7a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\widehat{p}-Z_{\\alpha\/2}\\sqrt{\\frac{\\widehat{p}(1-\\widehat{p})}{n}}\\ , \\ \\widehat{p}+Z_{\\alpha\/2}\\sqrt{\\frac{\\widehat{p}(1-\\widehat{p})}{n}}\\right) \" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"339\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<p>\u8981\u67e5\u770b\u5982\u4f55\u4f30\u8ba1\u4eba\u53e3\u6bd4\u4f8b\uff0c\u8bf7\u5355\u51fb\u4ee5\u4e0b\u94fe\u63a5\uff1a <\/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\/\u6bd4\u4f8b\u7684\u7f6e\u4fe1\u533a\u95f4\/\">\u4eba\u53e3\u6bd4\u4f8b\u7684\u7f6e\u4fe1\u533a\u95f4<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-proporciones\"><\/span>\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5c06\u4e86\u89e3\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03\u7684\u7ec4\u6210\uff0c\u56e0\u4e3a\u5b83\u662f\u4e0e\u62bd\u6837\u6bd4\u4f8b\u76f8\u5173\u7684\u7edf\u8ba1\u6982\u5ff5\u3002<\/p>\n<p>\u9996\u5148\uff0c\u6211\u4eec\u9996\u5148\u5b9a\u4e49\u4ec0\u4e48\u662f\u62bd\u6837\u5206\u5e03\u3002<strong>\u62bd\u6837\u5206\u5e03<\/strong>\u662f\u8003\u8651\u7edf\u8ba1\u603b\u4f53\u4e2d\u6240\u6709\u53ef\u80fd\u6837\u672c\u800c\u5f97\u51fa\u7684\u5206\u5e03\u3002<\/p>\n<p>\u56e0\u6b64\uff0c<strong>\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03<\/strong>\u662f\u901a\u8fc7\u8ba1\u7b97\u603b\u4f53\u4e2d\u6bcf\u4e2a\u53ef\u80fd\u6837\u672c\u7684\u6bd4\u4f8b\u800c\u5f97\u5230\u7684\u5206\u5e03\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5982\u679c\u6211\u4eec\u7814\u7a76\u4e00\u4e2a\u603b\u4f53\u4e2d\u6240\u6709\u53ef\u80fd\u7684\u6837\u672c\u5e76\u8ba1\u7b97\u6bcf\u4e2a\u6837\u672c\u7684\u6bd4\u4f8b\uff0c\u5219\u8ba1\u7b97\u51fa\u7684\u4e00\u7ec4\u503c\u5c31\u662f\u6837\u672c\u6bd4\u4f8b\u7684\u62bd\u6837\u5206\u5e03\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u7edf\u8ba1\u5b66\u4e2d\u7684\u6837\u672c\u6bd4\u4f8b\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u6837\u672c\u6bd4\u4f8b\u3001\u5df2\u89e3\u51b3\u7684\u7ec3\u4e60\uff0c\u4ee5\u53ca\u6837\u672c\u6bd4\u4f8b\u548c\u603b\u4f53\u6bd4\u4f8b\u4e4b\u95f4\u7684 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