{"id":243,"date":"2023-08-03T17:38:49","date_gmt":"2023-08-03T17:38:49","guid":{"rendered":"https:\/\/statorials.org\/cn\/%e5%b9%b3%e5%9d%87%e5%80%bc%e7%9a%84%e7%bd%ae%e4%bf%a1%e5%8c%ba%e9%97%b4\/"},"modified":"2023-08-03T17:38:49","modified_gmt":"2023-08-03T17:38:49","slug":"%e5%b9%b3%e5%9d%87%e5%80%bc%e7%9a%84%e7%bd%ae%e4%bf%a1%e5%8c%ba%e9%97%b4","status":"publish","type":"post","link":"https:\/\/statorials.org\/cn\/%e5%b9%b3%e5%9d%87%e5%80%bc%e7%9a%84%e7%bd%ae%e4%bf%a1%e5%8c%ba%e9%97%b4\/","title":{"rendered":"\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4"},"content":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u540c\u6837\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u4ee5\u53ca\u5206\u6b65\u7ec3\u4e60\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-el-intervalo-de-confianza-para-la-media\"><\/span>\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u662f\u591a\u5c11\uff1f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4<\/strong>\u662f\u4e3a\u603b\u4f53\u5747\u503c\u63d0\u4f9b\u5141\u8bb8\u503c\u8303\u56f4\u7684\u533a\u95f4\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\uff0c\u5b83\u4eec\u4e4b\u95f4\u5c06\u603b\u4f53\u5e73\u5747\u503c\u4e0e\u8bef\u5dee\u5e45\u5ea6\u8054\u7cfb\u8d77\u6765\u3002<\/p>\n<p>\u4f8b\u5982\uff0c\u5982\u679c\u603b\u4f53\u5e73\u5747\u503c\u7684 95% \u7f6e\u4fe1\u533a\u95f4\u4e3a (6.10)\uff0c\u5219\u8fd9\u610f\u5473\u7740 95% \u7684\u60c5\u51b5\u4e0b\u603b\u4f53\u5e73\u5747\u503c\u5c06\u5728 6 \u5230 10 \u4e4b\u95f4\u3002<\/p>\n<p>\u56e0\u6b64\uff0c\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u7528\u4e8e\u4f30\u8ba1\u603b\u4f53\u5e73\u5747\u503c\u6240\u5728\u7684\u4e24\u4e2a\u503c\u3002\u56e0\u6b64\uff0c\u5f53\u6240\u6709\u503c\u90fd\u672a\u77e5\u65f6\uff0c\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u5bf9\u4e8e\u8fd1\u4f3c\u603b\u4f53\u5747\u503c\u975e\u5e38\u6709\u7528\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-del-intervalo-de-confianza-para-la-media\"><\/span>\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5047\u8bbe<a href=\"https:\/\/statorials.org\/cn\/\u5178\u578b\u5316\/\">\u8f93\u5165\u53d8\u91cf<\/a>\u7684\u8fc7\u7a0b\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-f93a5e76c38b2e2556bd62ba66db5947_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{X-\\mu}{\\displaystyle\\frac{\\sigma}{\\sqrt{n}}} \\sim N(0,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"165\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p>\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u662f\u901a\u8fc7\u5728\u6837\u672c\u5e73\u5747\u503c\u4e2d\u52a0\u4e0a\u548c\u51cf\u53bb Z <sub>\u03b1\/2<\/sub>\u7684\u503c\u4e58\u4ee5\u6807\u51c6\u5dee (\u03c3) \u518d\u9664\u4ee5\u6837\u672c\u5927\u5c0f (n) \u7684\u5e73\u65b9\u6839\u6765\u8ba1\u7b97\u7684\u3002\u56e0\u6b64\uff0c\u5747\u503c\u7f6e\u4fe1\u533a\u95f4\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-985a374c69b468deb3d6d159fcbe6de5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\overline{x}-z_{\\alpha\/2}\\cdot \\frac{\\sigma}{\\sqrt{n}} \\ , \\ \\overline{x}+z_{\\alpha\/2}\\cdot \\frac{\\sigma}{\\sqrt{n}} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"251\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u5bf9\u4e8e\u5927\u6837\u672c\u91cf\u548c 95% \u7f6e\u4fe1\u6c34\u5e73\uff0c\u4e34\u754c\u503c\u4e3a Z <sub>\u03b1\/2<\/sub> = 1.96\uff1b\u5bf9\u4e8e 99% \u7f6e\u4fe1\u6c34\u5e73\uff0c\u4e34\u754c\u503c\u4e3a Z <sub>\u03b1\/2<\/sub> = 2.576\u3002<\/p>\n<p>\u5f53\u603b\u4f53\u65b9\u5dee\u5df2\u77e5\u65f6\uff0c\u4f7f\u7528\u4e0a\u8ff0\u516c\u5f0f\u3002\u4f46\u662f\uff0c\u5982\u679c\u603b\u4f53\u65b9\u5dee\u672a\u77e5\uff08\u8fd9\u662f\u6700\u5e38\u89c1\u7684\u60c5\u51b5\uff09\uff0c<strong>\u5219\u4f7f\u7528\u4ee5\u4e0b\u516c\u5f0f\u8ba1\u7b97\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\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-e40e2c40fbfe4f5aa96c21ff979aae5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\overline{x}-t_{\\alpha\/2}\\cdot \\frac{s}{\\sqrt{n}} \\ , \\ \\overline{x}+t_{\\alpha\/2}\\cdot \\frac{s}{\\sqrt{n}} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"247\" style=\"vertical-align: -17px;\"><\/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-33bd5d525ddf37600aef97b0c8c08f94_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t_{\\alpha\/2}\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"29\" style=\"vertical-align: -8px;\"><\/p>\n<p>\u662f n-1 \u4e2a\u81ea\u7531\u5ea6\u7684 Student t \u5206\u5e03\u7684\u503c\uff0c\u6982\u7387\u4e3a \u03b1\/2\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\u6837\u672c\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<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/intervalle-de-confiance.png\" alt=\"\u7f6e\u4fe1\u533a\u95f4\" class=\"wp-image-5249\" width=\"351\" height=\"339\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-un-intervalo-de-confianza-para-la-media\"><\/span>\u8ba1\u7b97\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u7684\u793a\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4e3a\u4e86\u8ba9\u60a8\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u603b\u4f53\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\uff0c\u6211\u4eec\u5728\u4e0b\u9762\u63d0\u4f9b\u4e86\u4e00\u4e2a\u9010\u6b65\u89e3\u51b3\u7684\u793a\u4f8b\u3002<\/p>\n<ul>\n<li>\u6211\u4eec\u6709 8 \u4e2a\u89c2\u6d4b\u503c\u7684\u6837\u672c\uff0c\u5176\u503c\u5982\u4e0b\u6240\u793a\u3002 95% \u7f6e\u4fe1\u6c34\u5e73\u4e0b\u603b\u4f53\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u662f\u591a\u5c11\uff1f<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"> 206 203 201 212<br \/> 194 176 208 201<\/p>\n<p>\u6b63\u5982\u6211\u4eec\u5728\u4e0a\u4e00\u8282\u4e2d\u770b\u5230\u7684\uff0c\u5f53\u6211\u4eec\u4e0d\u77e5\u9053\u603b\u4f53\u6807\u51c6\u5dee\u65f6\uff0c\u83b7\u53d6\u603b\u4f53\u5747\u503c\u7f6e\u4fe1\u533a\u95f4\u7684\u516c\u5f0f\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-e40e2c40fbfe4f5aa96c21ff979aae5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\overline{x}-t_{\\alpha\/2}\\cdot \\frac{s}{\\sqrt{n}} \\ , \\ \\overline{x}+t_{\\alpha\/2}\\cdot \\frac{s}{\\sqrt{n}} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"247\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p>\u6240\u4ee5\uff0c\u4e3a\u4e86\u786e\u5b9a\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\uff0c\u6211\u4eec\u9996\u5148\u8981\u8ba1\u7b97\u6837\u672c\u5747\u503c\u548c\u6807\u51c6\u5dee\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-e4db3aa9e4a141ef4ac81e1816a243ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}\\mu =200,13 \\\\[4ex]s=11,13\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"87\" style=\"vertical-align: 0px;\"><\/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\/\u7b97\u672f\u5e73\u5747\u6570\/\">\u7b97\u672f\u5e73\u5747\u503c\u8ba1\u7b97\u5668<\/a><br \/><span style=\"color:#ff951b\">\u27a4<\/span><strong>\u8bf7\u53c2\u9605\uff1a<\/strong><a href=\"https:\/\/statorials.org\/cn\/\u6807\u51c6\u5dee\u6216\u6807\u51c6\u5dee\/\">\u6807\u51c6\u5dee\u8ba1\u7b97\u5668<\/a><\/div>\n<p>\u7531\u4e8e\u6211\u4eec\u60f3\u8981\u627e\u5230\u7f6e\u4fe1\u6c34\u5e73\u4e3a 1-\u03b1=95% \u4e14\u6837\u672c\u91cf\u4e3a 8 \u7684\u7f6e\u4fe1\u533a\u95f4\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u8bbf\u95ee Student t \u5206\u5e03\u8868\u5e76\u67e5\u770b\u54ea\u4e2a\u503c\u5bf9\u5e94\u4e8e t <sub>0.025|7<\/sub> \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-776a555edd1d064cf29a3a354caa5325_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1-\\alpha=0,95 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\alpha=0,05 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\alpha\/2=0,025\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"534\" style=\"vertical-align: -5px;\"><\/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-2caa8c4576ebc261acfdb1341dc4567d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}t_{\\alpha\/2| n-1}= \\ \\color{orange}\\bm{?}\\\\[4ex]t_{0,025| 7}=2,365\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"72\" width=\"152\" style=\"vertical-align: 0px;\"><\/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\/\u5b66\u751ft\u5206\u5e03\u8868\/\">Student t \u5206\u5e03\u8868\u7684\u503c<\/a><\/div>\n<p>\u56e0\u6b64\uff0c\u6211\u4eec\u5e94\u7528\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u516c\u5f0f\u5e76\u6267\u884c\u8ba1\u7b97\u6765\u627e\u5230\u533a\u95f4\u7684\u6781\u9650\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-e40e2c40fbfe4f5aa96c21ff979aae5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\overline{x}-t_{\\alpha\/2}\\cdot \\frac{s}{\\sqrt{n}} \\ , \\ \\overline{x}+t_{\\alpha\/2}\\cdot \\frac{s}{\\sqrt{n}} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"247\" style=\"vertical-align: -17px;\"><\/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-7c9bc920ed22b19f5b15528eef268878_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(200,13-2,365\\cdot \\frac{11,13}{\\sqrt{8}} \\ , \\ 200,13+2,365\\cdot \\frac{11,13}{\\sqrt{8}} \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"394\" style=\"vertical-align: -17px;\"><\/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-322fdcebe92ea2e3868440918d39d431_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(190,82 \\ , \\ 209,43 \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p>\u603b\u4e4b\uff0c\u8ba1\u7b97\u51fa\u7684\u7f6e\u4fe1\u533a\u95f4\u544a\u8bc9\u6211\u4eec\uff0c\u7f6e\u4fe1\u6c34\u5e73\u4e3a 95% \u65f6\uff0c\u603b\u4f53\u5e73\u5747\u503c\u5c06\u5728 190.82 \u5230 209.43 \u4e4b\u95f4\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u6587\u89e3\u91ca\u4e86\u7edf\u8ba1\u5b66\u4e2d\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u662f\u4ec0\u4e48\u4ee5\u53ca\u5b83\u7684\u7528\u9014\u3002\u540c\u6837\uff0c\u60a8\u5c06\u4e86\u89e3\u5982\u4f55\u8ba1\u7b97\u5e73\u5747\u503c\u7684\u7f6e\u4fe1\u533a\u95f4\u4ee5\u53ca\u5206\u6b65\u7ec3\u4e60\u3002 \u5e73\u5747 [&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-243","post","type-post","status-publish","format-standard","hentry","category-14"],"yoast_head":"<!-- This site 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