{"id":279,"date":"2023-08-03T05:14:26","date_gmt":"2023-08-03T05:14:26","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%8a%bd%e6%a0%b7%e6%af%94%e4%be%8b%e5%88%86%e5%b8%83\/"},"modified":"2023-08-03T05:14:26","modified_gmt":"2023-08-03T05:14:26","slug":"%e6%8a%bd%e6%a0%b7%e6%af%94%e4%be%8b%e5%88%86%e5%b8%83","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%8a%bd%e6%a0%b7%e6%af%94%e4%be%8b%e5%88%86%e5%b8%83\/","title":{"rendered":"\u6bd4\u4f8b\u62bd\u6837\u5206\u914d"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u4ec0\u4e48\u662f\u7edf\u8ba1\u5b66\u4e2d\u7684\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03\u3002\u540c\u6837\uff0c\u60a8\u5c06\u627e\u5230\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03\u516c\u5f0f\uff0c\u6b64\u5916\u8fd8\u6709\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-distribucion-muestral-de-la-proporcion\"><\/span>\u6bd4\u4f8b\u7684\u62bd\u6837\u5206\u5e03\u662f\u600e\u6837\u7684\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03<\/strong>\uff08\u6216<strong>\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03<\/strong>\uff09\u662f\u901a\u8fc7\u8ba1\u7b97\u603b\u4f53\u4e2d\u6bcf\u4e2a\u53ef\u80fd\u6837\u672c\u7684\u6bd4\u4f8b\u800c\u5f97\u5230\u7684\u5206\u5e03\u3002\u5373\u603b\u4f53\u4e2d\u6240\u6709\u53ef\u80fd\u6837\u672c\u7684<a href=\"https:\/\/statorials.org\/cn\/\u6837\u672c\u6bd4\u4f8b\/\">\u62bd\u6837\u6bd4\u4f8b<\/a>\u6784\u6210\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03\u3002<\/p>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u6bd4\u4f8b\u7684\u62bd\u6837\u5206\u5e03\u662f\u901a\u8fc7\u7814\u7a76\u4e00\u4e2a\u603b\u4f53\u4e2d\u6240\u6709\u53ef\u4ee5\u9009\u62e9\u7684\u6837\u672c\u5e76\u63a8\u5bfc\u6bcf\u4e2a\u6837\u672c\u7684\u62bd\u6837\u6bd4\u4f8b\u6765\u83b7\u5f97\u7684\u3002\u8fd9\u6837\uff0c\u8ba1\u7b97\u51fa\u7684\u6837\u672c\u6bd4\u4f8b\u7684\u96c6\u5408\u5c31\u6784\u6210\u4e86\u8be5\u6bd4\u4f8b\u7684\u62bd\u6837\u5206\u5e03\u3002<\/p>\n<p>\u5982\u679c\u60a8\u60f3\u77e5\u9053\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03\u7684\u7528\u9014\uff0c\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u5b83\u7528\u4e8e\u8ba1\u7b97\u5728\u5206\u6790\u5355\u4e2a\u6837\u672c\u65f6\u63a5\u8fd1\u603b\u4f53\u6bd4\u4f8b\u503c\u7684\u6982\u7387\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\u7684\u62bd\u6837\u5206\u5e03\/\">\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-muestral-de-la-proporcion\"><\/span>\u6bd4\u4f8b\u62bd\u6837\u5206\u914d\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e8b\u5b9e\u4e0a\uff0c\u5f53\u6211\u4eec\u7814\u7a76\u4e00\u90e8\u5206\u6837\u672c\u65f6\uff0c\u6211\u4eec\u662f\u5728\u5206\u6790\u6210\u529f\u6848\u4f8b\u3002\u56e0\u6b64\uff0c\u7814\u7a76\u4e2d\u7684\u968f\u673a\u53d8\u91cf\u670d\u4ece<a href=\"https:\/\/statorials.org\/cn\/\u4e8c\u9879\u5206\u5e03-1\/\">\u4e8c\u9879\u5f0f\u6982\u7387\u5206\u5e03<\/a>\u3002<\/p>\n<p>\u6839\u636e\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\uff0c\u5bf9\u4e8e\u5927\u5c3a\u5bf8\uff08n&gt;30\uff09\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u4e8c\u9879\u5f0f\u5206\u5e03\u66f4\u63a5\u8fd1\u6b63\u6001\u5206\u5e03\u3002\u56e0\u6b64\uff0c<strong>\u6bd4\u4f8b\u7684\u62bd\u6837\u5206\u5e03\u8fd1\u4f3c\u4e8e\u5177\u6709\u4ee5\u4e0b\u53c2\u6570\u7684\u6b63\u6001\u5206\u5e03\uff1a<\/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-f3408076893f390bb65baecfe38e6eff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle\\mu_{p}=p \\qquad \\sigma_{p}=\\sqrt{\\frac{pq}{n}}\\\\[4ex]\\displaystyle N_{p}\\left(p, \\sqrt{\\frac{pq}{n}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"109\" width=\"168\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u91d1\u5b50<\/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-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\u6210\u529f\u7684\u6982\u7387\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-420eca7b6df080cc5f01773d1978f44a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u5931\u8d25\u7684\u6982\u7387<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e1d214c21abe0d79fa453d635a025865_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q=1-p\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u3002<\/p>\n<p><strong>\u6ce8\u610f\uff1a<\/strong>\u4e8c\u9879\u5f0f\u5206\u5e03\u53ea\u80fd\u8fd1\u4f3c\u4e8e\u6b63\u6001\u5206\u5e03\uff0c\u5982\u679c<\/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-88e275a965c091eb810599a07b0f8d46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n>30&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;14&#8243; width=&#8221;52&#8243; style=&#8221;vertical-align: -2px;&#8221;><\/p>\n<p>,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-41130f51ca4b83f1bf25b9dde90ecbfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"np\\ge 5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u548c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0af2ac5b6eb874f65b406b3bc39f0c7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"nq\\ge 5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"51\" style=\"vertical-align: -4px;\"><\/p>\n<p>\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\/\u6b63\u6001\u5206\u5e03\/\">\u6b63\u6001\u5206\u5e03\u793a\u4f8b<\/a><\/div>\n<p>\u56e0\u6b64\uff0c\u7531\u4e8e\u6bd4\u4f8b\u7684\u62bd\u6837\u5206\u5e03\u53ef\u4ee5\u8fd1\u4f3c\u4e3a\u6b63\u6001\u5206\u5e03\uff0c<strong>\u56e0\u6b64\u8ba1\u7b97\u4e0e\u6837\u672c\u6bd4\u4f8b\u76f8\u5173\u7684\u4efb\u4f55\u6982\u7387\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-5b7a4224240587268d0dd7865a33ac31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{pq}{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"78\" 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 style=\"margin-bottom:5px\">\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:5px\">\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\u4eba\u53e3\u7684\u6bd4\u4f8b\u3002<\/li>\n<li style=\"margin-bottom:5px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-420eca7b6df080cc5f01773d1978f44a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u603b\u4f53\u5931\u8d25\u7684\u6982\u7387\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e1d214c21abe0d79fa453d635a025865_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q=1-p\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"72\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u3002<\/li>\n<li style=\"margin-bottom:5px\">\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 style=\"margin-bottom:5px\">\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\u7531\u6807\u51c6\u6b63\u6001\u5206\u5e03 N(0,1) \u5b9a\u4e49\u7684\u53d8\u91cf\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-distribucion-muestral-de-la-proporcion\"><\/span>\u6bd4\u4f8b\u62bd\u6837\u5206\u914d\u7684\u5177\u4f53\u4f8b\u5b50<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03\u7684\u5b9a\u4e49\u53ca\u5176\u76f8\u5173\u516c\u5f0f\uff0c\u4e0b\u9762\u5c06\u7ed9\u51fa\u9010\u6b65\u89e3\u51b3\u7684\u793a\u4f8b\uff0c\u4ee5\u5145\u5206\u7406\u89e3\u8be5\u6982\u5ff5\u3002<\/p>\n<ul>\n<li>\u4e00\u5bb6\u5de5\u4e1a\u516c\u53f8\u4ece\u4e00\u5bb6\u5de5\u5382\u8d2d\u4e70\u4e00\u6279\u96f6\u4ef6\uff0c\u8be5\u5de5\u5382\u58f0\u79f0\u751f\u4ea7\u7684\u96f6\u4ef6\u53ea\u6709 3% \u7684\u7f3a\u9677\u96f6\u4ef6\u3002\u4e3a\u4e86\u9a8c\u8bc1\u8fd9\u4e00\u70b9\uff0c\u8be5\u516c\u53f8\u51b3\u5b9a\u5206\u6790\u4e00\u4efd\u5305\u542b 500 \u4e2a\u96f6\u4ef6\u7684\u8ba2\u5355\u3002\u5728\u6837\u672c\u4e2d\u53d1\u73b0\u8d85\u8fc7 5% \u7684\u7f3a\u9677\u90e8\u4ef6\u7684\u6982\u7387\u662f\u591a\u5c11\uff1f<\/li>\n<\/ul>\n<p>\u5728\u672c\u4f8b\u4e2d\uff0c\u6211\u4eec\u5e0c\u671b\u7814\u7a76\u7684\u603b\u4f53\u6bd4\u4f8b\u4e3a 0.03\uff0c\u56e0\u6b64\u53c2\u6570 q \u76f8\u5f53\u4e8e 0.97\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-f4354c268853ec7b592bcacd23f3b214_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}p=0,03\\\\[2ex]q=1-p=0,97\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"130\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4e3a\u4e86\u627e\u5230\u4ed6\u4eec\u8be2\u95ee\u6211\u4eec\u7684\u6982\u7387\uff0c\u6211\u4eec\u5fc5\u987b\u5e94\u7528\u4e0a\u4e00\u8282\u4e2d\u770b\u5230\u7684\u516c\u5f0f\u6765\u8ba1\u7b97\u76f8\u5e94\u7684\u7edf\u8ba1\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-647d67d275bb8a7fbeb60f7ae464c0fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{pq}{n}}}=\\cfrac{0,05-0,03}{\\displaystyle\\sqrt{\\frac{0,03\\cdot 0,97}{500}}}=2,62\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"264\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u83b7\u5f97\u8d85\u8fc7 5% \u7f3a\u9677\u96f6\u4ef6\u7684\u6982\u7387\u76f8\u5f53\u4e8e\u4ee5\u4e0b\u6982\u7387\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-a5e5cff61f2cc97762df561b3e35a7ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\\left[\\widehat{p}>0,05\\right]=P[Z>2,62]=1-P[Z\\leq 2,62]&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;360&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<p>\u6700\u540e\uff0c\u6211\u4eec\u5728<a 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