{"id":288,"date":"2023-08-03T02:21:11","date_gmt":"2023-08-03T02:21:11","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%8a%bd%e6%a0%b7%e5%88%86%e5%b8%831\/"},"modified":"2023-08-03T02:21:11","modified_gmt":"2023-08-03T02:21:11","slug":"%e6%8a%bd%e6%a0%b7%e5%88%86%e5%b8%831","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%8a%bd%e6%a0%b7%e5%88%86%e5%b8%831\/","title":{"rendered":"\u62bd\u6837\u5206\u914d"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u62bd\u6837\u5206\u5e03\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u62bd\u6837\u5206\u5e03\u7684\u542b\u4e49\u3001\u62bd\u6837\u5206\u5e03\u7684\u5177\u4f53\u793a\u4f8b\uff0c\u4ee5\u53ca\u6700\u5e38\u89c1\u7c7b\u578b\u62bd\u6837\u5206\u5e03\u7684\u516c\u5f0f\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-muestral\"><\/span>\u4ec0\u4e48\u662f\u62bd\u6837\u5206\u5e03\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u62bd\u6837\u5206\u5e03<\/strong>\u6216<strong>\u62bd\u6837\u5206\u5e03<\/strong>\u662f\u8003\u8651\u603b\u4f53\u4e2d\u6240\u6709\u53ef\u80fd\u6837\u672c\u800c\u5f97\u51fa\u7684\u5206\u5e03\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u62bd\u6837\u5206\u5e03\u662f\u901a\u8fc7\u8ba1\u7b97\u603b\u4f53\u4e2d\u6240\u6709\u53ef\u80fd\u6837\u672c\u7684\u62bd\u6837\u53c2\u6570\u5f97\u5230\u7684\u5206\u5e03\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u6211\u4eec\u4ece\u7edf\u8ba1\u603b\u4f53\u4e2d\u63d0\u53d6\u6240\u6709\u53ef\u80fd\u7684\u6837\u672c\u5e76\u8ba1\u7b97\u6bcf\u4e2a\u6837\u672c\u7684\u5747\u503c\uff0c\u5219\u6837\u672c\u5747\u503c\u96c6\u5408\u5f62\u6210\u62bd\u6837\u5206\u5e03\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u7531\u4e8e\u8ba1\u7b97\u7684\u53c2\u6570\u662f\u7b97\u672f\u5e73\u5747\u503c\uff0c\u56e0\u6b64\u5b83\u662f\u5e73\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u3002<\/p>\n<p>\u5728\u7edf\u8ba1\u5b66\u4e2d\uff0c\u62bd\u6837\u5206\u5e03\u7528\u4e8e\u8ba1\u7b97\u7814\u7a76\u5355\u4e2a\u6837\u672c\u65f6\u63a5\u8fd1\u603b\u4f53\u53c2\u6570\u503c\u7684\u6982\u7387\u3002\u540c\u6837\uff0c\u62bd\u6837\u5206\u5e03\u5141\u8bb8\u6211\u4eec\u4f30\u8ba1\u7ed9\u5b9a\u6837\u672c\u91cf\u7684\u62bd\u6837\u8bef\u5dee\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-distribucion-muestral\"><\/span>\u62bd\u6837\u5206\u5e03\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u73b0\u5728\u6211\u4eec\u77e5\u9053\u4e86\u62bd\u6837\u5206\u5e03\u7684\u5b9a\u4e49\uff0c\u8ba9\u6211\u4eec\u770b\u4e00\u4e2a\u7b80\u5355\u7684\u4f8b\u5b50\u6765\u5145\u5206\u7406\u89e3\u8fd9\u4e2a\u6982\u5ff5\u3002<\/p>\n<ul>\n<li>\u5728\u4e00\u4e2a\u76d2\u5b50\u91cc\uff0c\u6211\u4eec\u653e\u5165\u4e09\u4e2a\u7403\uff0c\u6bcf\u4e2a\u7403\u90fd\u6709\u4e00\u4e2a\u4ece 1 \u5230 3 \u7684\u6570\u5b57\uff0c\u8fd9\u6837\u4e00\u4e2a\u7403\u7684\u6570\u5b57\u4e3a 1\uff0c\u53e6\u4e00\u4e2a\u7403\u7684\u6570\u5b57\u4e3a 2\uff0c\u6700\u540e\u4e00\u4e2a\u7403\u7684\u6570\u5b57\u4e3a 3\u3002\u5bf9\u4e8e\u5927\u5c0f\u4e3a n = \u7684\u6837\u672c2\u3001\u5982\u679c\u9009\u62e9\u6709\u653e\u56de\u7684\u6837\u672c\uff0c\u5219\u8ba1\u7b97\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u7684\u6982\u7387\u3002<\/li>\n<\/ul>\n<p>\u6837\u672c\u7684\u9009\u62e9\u662f\u653e\u56de\u7684\uff0c\u5373\u62fe\u53d6\u6837\u672c\u4e2d\u7b2c\u4e00\u4e2a\u5143\u7d20\u7684\u7403\u8fd4\u56de\u5230\u76d2\u5b50\u4e2d\uff0c\u5e76\u53ef\u4ee5\u5728\u7b2c\u4e8c\u6b21\u63d0\u53d6\u65f6\u518d\u6b21\u9009\u62e9\u3002\u56e0\u6b64\uff0c\u603b\u4f53\u4e2d\u6240\u6709\u53ef\u80fd\u7684\u6837\u672c\u4e3a\uff1a<\/p>\n<p class=\"has-text-align-center\"> 1.1 1.2 1.3<br \/> 2.1 2.2 2.3<br \/> 3.1 3.2 3.3<\/p>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u8ba1\u7b97\u6bcf\u4e2a\u53ef\u80fd\u6837\u672c\u7684\u7b97\u672f\u5e73\u5747\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-36b3a1e0bbb1be6eddc1a5d9899c5643_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{11}=\\cfrac{1+1}{2}=1\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/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-ff446066e6102f75d2d5435ad9dc46d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,2) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{12}=\\cfrac{1+2}{2}=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/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-904c1ee161fd7214c2c20ef15a038ea2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,3) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{13}=\\cfrac{1+3}{2}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/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-4669b3b3d3ca07f035456cc50110134f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{21}=\\cfrac{2+1}{2}=1,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/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-9fae1b39671fce31802b9ff66c8c1b9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2,2) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{22}=\\cfrac{2+2}{2}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/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-fb036db8580a0d7389daddf6a938c541_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(2,3) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{23}=\\cfrac{2+3}{2}=2,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/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-7b77da5430a43732726cc62fb0fffe78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,1) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{31}=\\cfrac{3+1}{2}=2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"295\" style=\"vertical-align: -12px;\"><\/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-5edbfa4f2b8752676ceba5ad0cd34d6d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,2) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{32}=\\cfrac{3+2}{2}=2,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"311\" style=\"vertical-align: -12px;\"><\/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-bb60dfff5e3c5c090e019253ee84b198_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,3) \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\overline{x}_{33}=\\cfrac{3+3}{2}=3\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"296\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u56e0\u6b64\uff0c\u4ece\u603b\u4f53\u4e2d\u968f\u673a\u9009\u53d6\u6837\u672c\u65f6\uff0c\u83b7\u5f97\u6837\u672c\u5747\u503c\u5404\u503c\u7684\u6982\u7387\u5982\u4e0b\uff1a <\/p>\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\/table-de-distribution-dechantillonnage.png\" alt=\"\u6837\u672c\u5206\u5e03\u8868\u793a\u4f8b\" class=\"wp-image-6145\" width=\"166\" height=\"195\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p>\u4e0a\u8868\u4e2d\u6240\u793a\u7684\u62bd\u6837\u5206\u5e03\u7684\u6982\u7387\u662f\u901a\u8fc7\u5c06\u5177\u6709\u6240\u8ff0\u5e73\u5747\u503c\u7684\u6837\u672c\u6570\u91cf\u9664\u4ee5\u53ef\u80fd\u60c5\u51b5\u7684\u603b\u6570\u6765\u8ba1\u7b97\u7684\u3002\u4f8b\u5982\uff1a\u5728\u4e5d\u79cd\u53ef\u80fd\u7684\u60c5\u51b5\u4e0b\uff0c\u6837\u672c\u5e73\u5747\u503c\u6709\u4e24\u79cd\u4e3a 1.5\uff0c\u56e0\u6b64 P(1.5)=2\/9\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-distribuciones-muestrales\"><\/span>\u62bd\u6837\u5206\u5e03\u7684\u7c7b\u578b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u62bd\u6837\u5206\u5e03\uff08\u6216\u62bd\u6837\u5206\u5e03\uff09\u53ef\u4ee5\u6839\u636e\u83b7\u5f97\u62bd\u6837\u53c2\u6570\u7684\u62bd\u6837\u53c2\u6570\u8fdb\u884c\u5206\u7c7b\u3002\u56e0\u6b64\uff0c\u6700\u5e38\u89c1\u7684\u5206\u5e03\u7c7b\u578b\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>\u5747\u503c\u62bd\u6837\u5206\u5e03<\/strong>\uff1a\u8fd9\u662f\u901a\u8fc7\u8ba1\u7b97\u6bcf\u4e2a\u6837\u672c\u7684\u7b97\u672f\u5e73\u5747\u503c\u800c\u5f97\u5230\u7684\u62bd\u6837\u5206\u5e03\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03<\/strong>\uff1a\u662f\u901a\u8fc7\u8ba1\u7b97\u6240\u6709\u6837\u672c\u7684\u6bd4\u4f8b\u5f97\u5230\u7684\u62bd\u6837\u5206\u5e03\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u65b9\u5dee\u62bd\u6837\u5206\u5e03<\/strong>\uff1a\u8fd9\u662f\u5f62\u6210\u6837\u672c\u4e2d\u6240\u6709\u65b9\u5dee\u96c6\u5408\u7684\u62bd\u6837\u5206\u5e03\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u5747\u503c\u5dee\u5f02\u62bd\u6837\u5206\u5e03<\/strong>\uff1a\u662f\u901a\u8fc7\u8ba1\u7b97\u4e24\u4e2a\u4e0d\u540c\u603b\u4f53\u7684\u6240\u6709\u53ef\u80fd\u6837\u672c\u7684\u5747\u503c\u4e4b\u95f4\u7684\u5dee\u5f02\u800c\u5f97\u51fa\u7684\u62bd\u6837\u5206\u5e03\u3002<\/span><\/li>\n<li style=\"margin-bottom:18px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03\u5dee\u5f02<\/strong>\uff1a\u662f\u901a\u8fc7\u4ece\u4e24\u4e2a\u603b\u4f53\u4e2d\u51cf\u53bb\u6240\u6709\u53ef\u80fd\u7684\u62bd\u6837\u6bd4\u4f8b\u800c\u83b7\u5f97\u7684\u62bd\u6837\u5206\u5e03\u3002<\/span><\/li>\n<\/ul>\n<p>\u4e0b\u9762\u66f4\u8be6\u7ec6\u5730\u89e3\u91ca\u4e86\u6bcf\u79cd\u7c7b\u578b\u7684\u62bd\u6837\u5206\u5e03\u3002 <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-media\"><\/span>\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u670d\u4ece\u6b63\u6001\u6982\u7387\u5206\u5e03\u4e14\u5747\u503c\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-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>\u548c\u6807\u51c6\u5dee<\/p>\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>\u5e76\u63d0\u53d6\u5c3a\u5bf8\u6837\u672c<\/p>\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>\uff0c\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u4e5f\u5c06\u7531\u5177\u6709\u4ee5\u4e0b\u7279\u5f81\u7684\u6b63\u6001\u5206\u5e03\u5b9a\u4e49\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-44571aa7337b095ab9c9fa1f746e93a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\mu_{\\overline{x}}=\\mu \\qquad \\sigma_{\\overline{x}}=\\cfrac{\\sigma}{\\sqrt{n}}\\\\[4ex]\\displaystyle N_{\\overline{x}}\\left(\\mu, \\frac{\\sigma}{\\sqrt{n}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"102\" width=\"159\" 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-8ed084decbdfb365889aae767cf63e81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_{\\overline{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"20\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u5e73\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u7684\u5e73\u5747\u503c\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9067e28d896c7e5278763081c6cc40d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_{\\overline{x}}\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"19\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u5b83\u7684\u6807\u51c6\u5dee\u3002\u6b64\u5916\uff0c<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7d78e2a2f2fae99a53eb087263cbb478_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{\\sigma}{\\sqrt{n}}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"26\" style=\"vertical-align: -16px;\"><\/p>\n<p>\u662f\u62bd\u6837\u5206\u5e03\u7684\u6807\u51c6\u8bef\u3002<\/p>\n<p><strong>\u6ce8\uff1a<\/strong>\u5982\u679c\u603b\u4f53\u4e0d\u670d\u4ece\u6b63\u6001\u5206\u5e03\u4f46\u6837\u672c\u91cf\u8f83\u5927\uff08n&gt;30\uff09\uff0c\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u4e5f\u53ef\u4ee5\u901a\u8fc7\u4e2d\u5fc3\u5b9a\u7406\u6781\u9650\u903c\u8fd1\u4e0a\u9762\u7684\u6b63\u6001\u5206\u5e03\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u7531\u4e8e\u5747\u503c\u7684\u62bd\u6837\u5206\u5e03\u9075\u5faa\u6b63\u6001\u5206\u5e03\uff0c<strong>\u56e0\u6b64\u8ba1\u7b97\u4e0e\u6837\u672c\u5747\u503c\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-ecd8bcb78b739c50d01b8bad563e5cb7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\overline{x}-\\mu}{\\displaystyle\\frac{\\sigma}{\\sqrt{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" 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 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-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 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-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>\u8fd9\u662f\u4eba\u53e3\u5e73\u5747\u503c\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-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\u603b\u4f53\u6807\u51c6\u5dee\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<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\u62bd\u6837\u5206\u5e03\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-proporcion\"><\/span>\u6bd4\u4f8b\u62bd\u6837\u5206\u914d<span class=\"ez-toc-section-end\"><\/span><\/h3>\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\u4e8c\u9879\u5f0f\u6982\u7387\u5206\u5e03\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<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<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\/\u62bd\u6837\u6bd4\u4f8b\u5206\u5e03\/\">\u5df2\u89e3\u51b3\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03\u7684\u7ec3\u4e60<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-varianza\"><\/span>\u65b9\u5dee\u62bd\u6837\u5206\u5e03<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u65b9\u5dee\u7684\u62bd\u6837\u5206\u5e03\u7531\u5361\u65b9\u6982\u7387\u5206\u5e03\u5b9a\u4e49\u3002\u56e0\u6b64\uff0c<strong>\u62bd\u6837\u65b9\u5dee\u5206\u5e03\u7684\u7edf\u8ba1\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\u62bd\u6837\u5206\u5e03\u7684\u7edf\u8ba1\u91cf\uff0c\u9075\u5faa\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\u603b\u4f53\u65b9\u5dee\u3002 <\/li>\n<\/ul>\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\/\u62bd\u6837\u65b9\u5dee\u5206\u5e03\/\">\u65b9\u5dee\u62bd\u6837\u5206\u5e03\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-diferencia-de-medias\"><\/span>\u5747\u503c\u5dee\u7684\u62bd\u6837\u5206\u5e03<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u5982\u679c\u6837\u672c\u91cf\u8db3\u591f\u5927\uff08n <sub>1<\/sub> \u226530\u4e14n <sub>2<\/sub> \u226530\uff09\uff0c\u5219\u5747\u5dee\u7684\u62bd\u6837\u5206\u5e03\u670d\u4ece\u6b63\u6001\u5206\u5e03\u3002\u66f4\u51c6\u786e\u5730\u8bf4\uff0c\u6240\u8ff0\u5206\u5e03\u7684\u53c2\u6570\u8ba1\u7b97\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-90c67b74b4e9326b7869d641a59725d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle \\mu_{\\overline{x_1}-\\overline{x_2}}=\\mu_1-\\mu_2 \\qquad \\sigma_{\\overline{x_1}-\\overline{x_2}}=\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}\\\\[6ex]\\displaystyle N_{\\overline{x_1}-\\overline{x_2}}\\left(\\mu_1-\\mu_2, \\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"328\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p><strong>\u6ce8\u610f\uff1a<\/strong>\u5982\u679c\u4e24\u4e2a\u603b\u4f53\u90fd\u662f\u6b63\u6001\u5206\u5e03\uff0c\u5219\u65e0\u8bba\u6837\u672c\u5927\u5c0f\u5982\u4f55\uff0c\u5747\u503c\u5dee\u7684\u62bd\u6837\u5206\u5e03\u90fd\u9075\u5faa\u6b63\u6001\u5206\u5e03\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u7531\u4e8e\u5747\u503c\u5dee\u7684\u62bd\u6837\u5206\u5e03\u662f\u7531\u6b63\u6001\u5206\u5e03\u5b9a\u4e49\u7684\uff0c<strong>\u56e0\u6b64\u5747\u503c\u5dee\u7684\u62bd\u6837\u5206\u5e03\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-767964a3f07b303178ee08ec191eef43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{(\\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=\"80\" 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 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-a4071a38558726a684ed069430c89fe2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6837\u672c i \u7684\u5e73\u5747\u503c\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-78e04dacbf6a47efcbdcc0417020dcbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u603b\u4f53 i \u7684\u5e73\u5747\u503c\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-dc8c8f782c0ed8b7925012b60e174fa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u603b\u4f53 i \u7684\u6807\u51c6\u5dee\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-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6837\u672c\u5927\u5c0f i\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<p>\u8bf7\u6ce8\u610f\uff0c\u6765\u81ea\u4e0d\u540c\u4eba\u7fa4\u7684\u6837\u672c\u53ef\u80fd\u5177\u6709\u4e0d\u540c\u7684\u6837\u672c\u91cf\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\u62bd\u6837\u5206\u5e03\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"distribucion-muestral-de-la-diferencia-de-proporciones\"><\/span>\u6bd4\u4f8b\u5dee\u5f02\u62bd\u6837\u5206\u5e03<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u4e3a\u6bd4\u4f8b\u62bd\u6837\u5206\u5e03\u5dee\u5f02\u9009\u62e9\u7684\u6837\u672c\u7531\u4e8c\u9879\u5f0f\u5206\u5e03\u5b9a\u4e49\uff0c\u56e0\u4e3a\u51fa\u4e8e\u5b9e\u9645\u76ee\u7684\uff0c\u6bd4\u4f8b\u662f\u6210\u529f\u6848\u4f8b\u4e0e\u89c2\u5bdf\u603b\u6570\u7684\u6bd4\u7387\u3002<\/p>\n<p>\u7136\u800c\uff0c\u7531\u4e8e\u4e2d\u5fc3\u6781\u9650\u5b9a\u7406\uff0c\u4e8c\u9879\u5f0f\u5206\u5e03\u53ef\u4ee5\u8fd1\u4f3c\u4e3a\u6b63\u6001\u6982\u7387\u5206\u5e03\u3002\u56e0\u6b64\uff0c\u6bd4\u4f8b\u5dee\u5f02\u7684\u62bd\u6837\u5206\u5e03\u53ef\u4ee5\u8fd1\u4f3c\u4e3a\u5177\u6709\u4ee5\u4e0b\u7279\u5f81\u7684\u6b63\u6001\u5206\u5e03\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-a1ce359b5dd6d80f8d27b0b9a1034bed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\displaystyle\\mu_{\\widehat{p_1}-\\widehat{p_2}}=p_1-p_2 \\qquad \\sigma_{\\widehat{p_1}-\\widehat{p_2}}=\\sqrt{\\frac{p_1q_1}{n_1}+\\frac{p_2q_2}{n_2}}\\\\[6ex]\\displaystyle N_{p}\\left(p_1-p_2, \\sqrt{\\frac{p_1q_1}{n_1}+\\frac{p_2q_2}{n_2}}\\right) \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"122\" width=\"348\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p><strong>\u6ce8\uff1a<\/strong>\u6bd4\u4f8b\u5dee\u5f02\u7684\u62bd\u6837\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-6a7ebccb76a4ee9bbf44bb0f41ffee53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1\\geq30\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -3px;\"><\/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-93c3febf2679c77d41d7b319e262f298_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2\\geq 30\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: -3px;\"><\/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-19a35b2095afa5133c32d92de163adaf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1p_1\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"67\" style=\"vertical-align: -4px;\"><\/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-a89c44bd89266e2fba37bf5211a6e30e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2p_2\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"67\" style=\"vertical-align: -4px;\"><\/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-08c0b04a830a0062f4e7f25801c45fa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1q_1\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" 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-789e8bfde9b6a18c7ff9b1390feca142_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2q_2\\geq5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u7531\u4e8e\u6bd4\u4f8b\u5dee\u7684\u62bd\u6837\u5206\u5e03\u53ef\u4ee5\u8fd1\u4f3c\u4e3a\u6b63\u6001\u5206\u5e03\uff0c<strong>\u56e0\u6b64\u6bd4\u4f8b\u5dee\u7684\u62bd\u6837\u5206\u5e03\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-a6b74dafd0599052a453e77646e5a77a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{(\\widehat{p_1}-\\widehat{p_2})-(p_1-p_2)}{\\displaystyle\\sqrt{\\frac{p_1q_1}{n_1}+\\frac{p_2q_2}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"198\" 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-ad10d8ae9a51401d94ca9742249d6d15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"15\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u6837\u672c\u6bd4\u4f8b i\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-a5db80b23c0dc6e4f21c509cb298856a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u4eba\u53e3 i \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-4b2d0075b0f4fd8e4e14194b33ed0fe8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q_i\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u662f\u7fa4\u4f53 i \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-917f2422b9b0d7d99ec3de548cc6bba3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q_i=1-p_i\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" 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-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6837\u672c\u5927\u5c0f i\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<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\u5dee\u5f02\u62bd\u6837\u5206\u5e03\/\">\u6bd4\u4f8b\u5dee\u62bd\u6837\u5206\u5e03\u7684\u5df2\u89e3\u51b3\u7ec3\u4e60<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u7684\u62bd\u6837\u5206\u5e03\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u4e86\u89e3\u62bd\u6837\u5206\u5e03\u7684\u542b\u4e49\u3001\u62bd\u6837\u5206\u5e03\u7684\u5177\u4f53\u793a\u4f8b\uff0c\u4ee5\u53ca\u6700\u5e38\u89c1\u7c7b [&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-288","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\/ 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