{"id":262,"date":"2023-08-03T11:07:43","date_gmt":"2023-08-03T11:07:43","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e6%af%94%e4%be%8b%e5%81%87%e8%ae%be%e6%a3%80%e9%aa%8c\/"},"modified":"2023-08-03T11:07:43","modified_gmt":"2023-08-03T11:07:43","slug":"%e6%af%94%e4%be%8b%e5%81%87%e8%ae%be%e6%a3%80%e9%aa%8c","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e6%af%94%e4%be%8b%e5%81%87%e8%ae%be%e6%a3%80%e9%aa%8c\/","title":{"rendered":"\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u5047\u8bbe\u68c0\u9a8c\u7684\u6bd4\u4f8b\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u627e\u5230\u8be5\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u516c\u5f0f\uff0c\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u4e00\u4e2a\u5206\u6b65\u7ec3\u4e60\uff0c\u4ee5\u5145\u5206\u7406\u89e3\u5b83\u662f\u5982\u4f55\u5b8c\u6210\u7684\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-prueba-de-hipotesis-para-la-proporcion\"><\/span>\u4ec0\u4e48\u662f\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c<\/strong>\u662f\u4e00\u79cd\u7edf\u8ba1\u65b9\u6cd5\uff0c\u7528\u4e8e\u786e\u5b9a\u662f\u5426\u62d2\u7edd\u603b\u4f53\u6bd4\u4f8b\u7684\u539f\u5047\u8bbe\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u6839\u636e\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u6bd4\u4f8b\u548c\u663e\u7740\u6027\u6c34\u5e73\u7684\u503c\uff0c\u62d2\u7edd\u6216\u63a5\u53d7\u539f\u5047\u8bbe\u3002<\/p>\n<p>\u8bf7\u6ce8\u610f\uff0c\u5047\u8bbe\u68c0\u9a8c\u4e5f\u53ef\u79f0\u4e3a\u5047\u8bbe\u5bf9\u6bd4\u3001\u5047\u8bbe\u68c0\u9a8c\u6216\u663e\u7740\u6027\u68c0\u9a8c\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-prueba-de-hipotesis-para-la-proporcion\"><\/span>\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7b49\u4e8e\u6837\u672c\u6bd4\u4f8b\u7684\u5dee\u503c\u51cf\u53bb\u6bd4\u4f8b\u7684\u5efa\u8bae\u503c\u9664\u4ee5\u6bd4\u4f8b\u7684\u6807\u51c6\u5dee\u3002<\/p>\n<p>\u56e0\u6b64<strong>\uff0c\u8be5\u6bd4\u4f8b\u7684\u68c0\u9a8c\u5047\u8bbe\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\u6bd4\u4f8b\u7684\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\u6b63\u6001\u5206\u5e03\u8868\u4e2d\u8f7b\u677e\u83b7\u5f97\u4e34\u754c\u503c\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>\u53c2\u89c1\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u6b63\u6001\u5206\u5e03\u8868\/\">\u6b63\u6001\u5206\u5e03\u8868<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-la-prueba-de-hipotesis-para-la-proporcion\"><\/span>\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e00\u65e6\u6211\u4eec\u4e86\u89e3\u4e86\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c\u7684\u5b9a\u4e49\u53ca\u5176\u516c\u5f0f\u662f\u4ec0\u4e48\uff0c\u6211\u4eec\u5c06\u89e3\u51b3\u4e00\u4e2a\u4f8b\u5b50\u6765\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e2a\u6982\u5ff5\u3002<\/p>\n<ul>\n<li>\u636e\u5176\u5236\u9020\u5546\u79f0\uff0c\u9488\u5bf9\u7279\u5b9a\u75be\u75c5\u7684\u836f\u7269\u6709 70% \u7684\u6709\u6548\u6027\u3002\u5728\u5b9e\u9a8c\u5ba4\u4e2d\uff0c\u6211\u4eec\u6d4b\u8bd5\u4e86\u8fd9\u79cd\u836f\u7269\u7684\u6709\u6548\u6027\uff0c\u56e0\u4e3a\u7814\u7a76\u4eba\u5458\u8ba4\u4e3a\u6bd4\u4f8b\u4e0d\u540c\u3002\u4e3a\u6b64\uff0c\u8be5\u836f\u7269\u5728 1,000 \u540d\u60a3\u8005\u6837\u672c\u4e0a\u8fdb\u884c\u4e86\u6d4b\u8bd5\uff0c\u5e76\u6cbb\u6108\u4e86 641 \u4eba\u3002\u5bf9\u603b\u4f53\u6bd4\u4f8b\u8fdb\u884c\u5047\u8bbe\u68c0\u9a8c\uff0c\u663e\u7740\u6027\u6c34\u5e73\u4e3a 5%\uff0c\u4ee5\u62d2\u7edd\u6216\u4e0d\u62d2\u7edd\u7814\u7a76\u4eba\u5458\u7684\u5047\u8bbe\u3002<\/li>\n<\/ul>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u4eba\u53e3\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u7684<a href=\"https:\/\/statorials.org\/cn\/\u96f6\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\/\">\u539f\u5047\u8bbe\u548c\u5907\u62e9<\/a>\u5047\u8bbe\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-f7da8281eeecc022e2ec7daea6a9756e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: p=0,70\\\\[2ex] H_1:p\\neq 0,70 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"117\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u6837\u672c\u4e2d\u88ab\u836f\u7269\u6cbb\u6108\u7684\u4eba\u6570\u6bd4\u4f8b\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-93865dbb1097265b35967f0138a51d89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}=\\cfrac{641}{1000}=0,641\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"137\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u6211\u4eec\u901a\u8fc7\u5e94\u7528\u4e0a\u9762\u7684\u516c\u5f0f\u6765\u8ba1\u7b97\u8be5\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\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-e689388b0a73e91c1e3d8812c2c4c42a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} \\displaystyle Z&amp;=\\frac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{p(1-p)}{n}}}\\\\[2ex]Z&amp;=\\frac{0,641-0,70}{\\displaystyle\\sqrt{\\frac{0,70\\cdot (1-0,70)}{1000}}}  \\\\[2ex] Z&amp;=-4,07\\end{aligned}}\" title=\"Rendered by QuickLaTeX.com\" height=\"195\" width=\"186\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u53e6\u4e00\u65b9\u9762\uff0c\u7531\u4e8e\u663e\u7740\u6027\u6c34\u5e73\u4e3a 0.05 \u5e76\u4e14\u8fd9\u662f\u53cc\u5c3e\u5047\u8bbe\u68c0\u9a8c\uff0c\u56e0\u6b64\u68c0\u9a8c\u7684\u4e34\u754c\u503c\u4e3a 1.96\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-f4aa318300c46315a36b7bbecbd57e02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z_{0,025}=1,96\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"102\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u663e\u7740\u6027\u6c34\u5e73\/\">\u663e\u7740\u6027\u6c34\u5e73 0.05<\/a><\/div>\n<p>\u603b\u4e4b\uff0c\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u7edd\u5bf9\u503c\u5927\u4e8e\u4e34\u754c\u503c\uff0c\u56e0\u6b64\u6211\u4eec\u62d2\u7edd\u539f\u5047\u8bbe\u5e76\u63a5\u53d7\u5907\u62e9\u5047\u8bbe\u3002 <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-06104fc4aa1cf5269aa8bc841cc05a9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|-4,07|=4,07>1,96 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Se rechaza } H_0&#8243; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;19&#8243; width=&#8221;424&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u5e73\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c\/\">\u5747\u503c\u7684\u5047\u8bbe\u68c0\u9a8c<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-de-hipotesis-para-las-proporciones-de-dos-muestras\"><\/span>\u4e24\u4e2a\u6837\u672c\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5bf9\u4e24\u4e2a\u6837\u672c\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c<\/strong>\u7528\u4e8e\u62d2\u7edd\u6216\u63a5\u53d7\u4e24\u4e2a\u4e0d\u540c\u603b\u4f53\u7684\u6bd4\u4f8b\u76f8\u7b49\u7684\u96f6\u5047\u8bbe\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u4e24\u4e2a\u6837\u672c\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u7684\u539f\u5047\u8bbe\u59cb\u7ec8\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-5572e3ad602776be8957247415435ef5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"H_0: p_1=p_2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"93\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u867d\u7136\u66ff\u4ee3\u5047\u8bbe\u53ef\u4ee5\u662f\u4ee5\u4e0b\u4e09\u4e2a\u9009\u9879\u4e4b\u4e00\uff1a<\/p>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\begin{array}{l}H_1:p_1\\neq p_2\\\\[2ex]H_1:p_1&gt;p_2\\\\[2ex]H_1:p_1 The combined ratio of the two samples is calculated as follows:[latex]p=\\cfrac {x_1+x_2}{n_1+n_2}\n\n*** Error message:\nMissing $ inserted.\nleading text: \\begin{array}{l}\nPlease use \\mathaccent for accents in math mode.\nleading text: ...H_1:p_1&gt;p_2\\\\[2ex]H_1:p_1 The combined ratio\nPlease use \\mathaccent for accents in math mode.\nleading text: ...\\[2ex]H_1:p_1 The combined ratio of the two\nPlease use \\mathaccent for accents in math mode.\nleading text: ...combined of the two samples is calculated\n\\begin{array} on input line 8 ended by \\end{document}.\nleading text: \\end{document}\nImproper \\prevdepth.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\cr inserted.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nYou can't use `\\end' in internal vertical mode.\n\n<\/pre>\n<p>\u4e24\u4e2a\u6837\u672c\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u8ba1\u7b97\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-27dc38fa4280149a55c46c6753204c9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\displaystyle \\frac{x_1}{n_1}-\\frac{x_2}{n_2}}{\\displaystyle \\sqrt{p(1-p)\\left(\\frac{1}{n_1}+\\frac{1}{n_2}\\right)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"94\" width=\"214\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\">\u91d1\u5b50\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-0be116875001706f29a24434bd0d91c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u662f\u4e24\u4e2a\u6837\u672c\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-d7aa45c8899989487fb32dab51a8f7d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6837\u672c 1 \u4e2d\u7684\u7ed3\u679c\u6570\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-de02251c2c969c17b8633e299d9a2244_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6837\u672c 2 \u4e2d\u7684\u7ed3\u679c\u6570\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-cebc0a013985f2695aeb53ded9e7afb1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6837\u672c\u91cf 1\u3002<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bf1e42c248eee22a0911c24c95fe28f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6837\u672c\u91cf 2\u3002<\/li>\n<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\u4e24\u4e2a\u6837\u672c\u7684\u603b\u6bd4\u4f8b\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-de-hipotesis-para-las-proporciones-de-k-muestras\"><\/span> k \u4e2a\u6837\u672c\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5728<strong>\u5173\u4e8e k \u4e2a\u6837\u672c\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u4e2d\uff0c<\/strong>\u76ee\u6807\u662f\u786e\u5b9a\u4e0d\u540c\u603b\u4f53\u7684\u6240\u6709\u6bd4\u4f8b\u662f\u5426\u76f8\u7b49\uff0c\u6216\u8005\u76f8\u53cd\uff0c\u662f\u5426\u5b58\u5728\u4e0d\u540c\u7684\u6bd4\u4f8b\u3002\u56e0\u6b64\uff0c\u672c\u4f8b\u4e2d\u7684\u539f\u5047\u8bbe\u548c\u5907\u62e9\u5047\u8bbe\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-77d7e13b427dd927953473a6bfbe9a55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\text{Todas las proporciones son iguales}\\\\[2ex] H_1: \\text{No todas las proporciones son iguales} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"341\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6240\u6709\u6837\u672c\u7684\u7ec4\u5408\u6bd4\u4f8b\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-bd6eafe24ac6e33f95c11428cdf34b29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p=\\cfrac{\\displaystyle\\sum_{i=1}^k x_i}{\\displaystyle\\sum_{i=1}^k n_i}=\\cfrac{x_1+x_2+\\dots+x_k}{n_1+n_2+\\dots+n_k}\" title=\"Rendered by QuickLaTeX.com\" height=\"113\" width=\"250\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p>\u67e5\u627e k \u4e2a\u6837\u672c\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u7684\u516c\u5f0f\u4e3a\uff1a <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bf14ba17db281bb65549da86f59a0b65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\chi^2 =\\sum_{i=1}^k \\frac{(x_i-e_i)^2}{e_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"52\" width=\"146\" style=\"vertical-align: -21px;\"><\/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-7213d98c216b76fca752271158e4c7e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\chi^2 = \\frac{(x_1-e_1)^2}{e_1} +\\frac{(x_2-e_2)^2}{e_2} +\\dots+\\frac{(x_k-e_k)^2}{e_k}\" title=\"Rendered by QuickLaTeX.com\" height=\"42\" width=\"371\" style=\"vertical-align: -15px;\"><\/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 k \u4e2a\u6837\u672c\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u7edf\u8ba1\u91cf\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7edf\u8ba1\u91cf\u670d\u4ece\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-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6837\u672c i \u4e2d\u7684\u7ed3\u679c\u6570\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-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>\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\u6240\u6709\u6837\u672c\u7684\u603b\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-550848dfdd05b5c6464d4e22fbf52486_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"13\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u662f\u6837\u672c i \u7684\u9884\u671f\u547d\u4e2d\u6570\u3002\u5b83\u662f\u901a\u8fc7\u4e58\u4ee5\u7ec4\u5408\u6bd4\u4f8b\u6765\u8ba1\u7b97\u7684<\/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>\u6309\u6837\u672c\u91cf<\/p>\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>\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u5047\u8bbe\u68c0\u9a8c\u7684\u6bd4\u4f8b\u3002\u56e0\u6b64\uff0c\u60a8\u5c06\u627e\u5230\u8be5\u6bd4\u4f8b\u7684\u5047\u8bbe\u68c0\u9a8c\u516c\u5f0f\uff0c\u6b64\u5916\uff0c\u60a8\u8fd8\u5c06\u627e\u5230\u4e00\u4e2a\u5206\u6b65\u7ec3\u4e60\uff0c\u4ee5\u5145\u5206\u7406\u89e3 [&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-262","post","type-post","status-publish","format-standard","hentry","category-14"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c<\/title>\n<meta name=\"description\" content=\"\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c\u3001\u5176\u516c\u5f0f\u4ee5\u53ca\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c\u7684\u5177\u4f53\u793a\u4f8b\u3002\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/cn\/\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c\/\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 \u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c\" \/>\n<meta property=\"og:description\" content=\"\u5728\u8fd9\u91cc\u60a8\u5c06\u4e86\u89e3\u4ec0\u4e48\u662f\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c\u3001\u5176\u516c\u5f0f\u4ee5\u53ca\u6bd4\u4f8b\u5047\u8bbe\u68c0\u9a8c\u7684\u5177\u4f53\u793a\u4f8b\u3002\" \/>\n<meta property=\"og:url\" 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