{"id":267,"date":"2023-08-03T08:29:13","date_gmt":"2023-08-03T08:29:13","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e3%82%b5%e3%83%b3%e3%83%95%e3%82%9a%e3%83%ab%e3%81%ae%e5%89%b2%e5%90%88\/"},"modified":"2023-08-03T08:29:13","modified_gmt":"2023-08-03T08:29:13","slug":"%e3%82%b5%e3%83%b3%e3%83%95%e3%82%9a%e3%83%ab%e3%81%ae%e5%89%b2%e5%90%88","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e3%82%b5%e3%83%b3%e3%83%95%e3%82%9a%e3%83%ab%e3%81%ae%e5%89%b2%e5%90%88\/","title":{"rendered":"\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7d71\u8a08\u306b\u304a\u3051\u308b\u6a19\u672c\u6bd4\u7387\u3068\u306f\u4f55\u304b\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6a19\u672c\u6bd4\u7387\u306e\u8a08\u7b97\u65b9\u6cd5\u3001\u89e3\u6c7a\u3055\u308c\u305f\u6f14\u7fd2\u3001\u3055\u3089\u306b\u6a19\u672c\u6bd4\u7387\u3068\u6bcd\u96c6\u56e3\u6bd4\u7387\u306e\u9055\u3044\u304c\u308f\u304b\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-proporcion-muestral\"><\/span>\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u306f\u3069\u306e\u304f\u3089\u3044\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387<\/strong>\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306b\u5bfe\u3059\u308b\u30b5\u30f3\u30d7\u30eb\u5185\u306e\u6210\u529f\u4e8b\u4f8b\u306e\u6bd4\u7387\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u5185\u306e\u6210\u529f\u6570\u3092\u30c7\u30fc\u30bf\u306e\u7dcf\u6570\u3067\u5272\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<p>\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387\u306e\u8a18\u53f7\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\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-ecd29d136a62fc6b274e1181e064e20e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u3002<\/p>\n<p>\u7d71\u8a08\u3067\u306f\u3001\u8abf\u67fb\u3092\u5b9f\u65bd\u3059\u308b\u5834\u5408\u3001\u901a\u5e38\u3001\u6bcd\u96c6\u56e3\u30c7\u30fc\u30bf\u306e\u3059\u3079\u3066\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u306e\u305f\u3081\u3001\u901a\u5e38\u306f\u4ee3\u8868\u7684\u306a\u30b5\u30f3\u30d7\u30eb\u306e\u7814\u7a76\u304c\u5b9f\u884c\u3055\u308c\u3001\u305d\u306e\u5f8c\u3001\u5c0e\u304d\u51fa\u3055\u308c\u305f\u7d50\u8ad6\u304c\u6bcd\u96c6\u56e3\u5168\u4f53\u306b\u5916\u633f\u3055\u308c\u307e\u3059\u3002\u4eba\u53e3\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u306f\u6bcd\u96c6\u56e3\u5168\u4f53\u306e\u5272\u5408\u3092\u63a8\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u4ee5\u4e0b\u3067\u306f\u3001\u3053\u308c\u304c\u3069\u306e\u3088\u3046\u306b\u884c\u308f\u308c\u308b\u304b\u3092\u898b\u3066\u3044\u304d\u307e\u3059\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\u7167:<\/strong><a href=\"https:\/\/statorials.org\/ja\/\u4ee3\u8868\u30b5\u30f3\u30d5\u309a\u30eb1\/\">\u4ee3\u8868\u7684\u306a\u30b5\u30f3\u30d7\u30eb\u3068\u306f\u4f55\u3067\u3059\u304b?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-proporcion-muestral\"><\/span>\u6bd4\u4f8b\u5f0f\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u5185\u306e\u6210\u529f\u30b1\u30fc\u30b9\u306e\u6570\u3092\u30b5\u30f3\u30d7\u30eb \u30b5\u30a4\u30ba\u3067\u5272\u3063\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387\u3092\u8a08\u7b97\u3059\u308b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b<\/strong>\u306a\u308a\u307e\u3059\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-8497d73f09738f45701a70350badaacd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}=\\cfrac{e}{n}\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"46\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\">\u91d1\uff1a<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:3px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ecd29d136a62fc6b274e1181e064e20e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u306f\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u3067\u3059\u3002<\/li>\n<li style=\"margin-bottom:3px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-558a73dc6903ad0c33580b0ce9f110d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u30b5\u30f3\u30d7\u30eb\u5185\u306e\u6210\u529f\u3057\u305f\u30b1\u30fc\u30b9\u306e\u6570\u3067\u3059\u3002<\/li>\n<li style=\"margin-bottom:3px\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p>\u30b5\u30f3\u30d7\u30eb\u5185\u306e\u30c7\u30fc\u30bf\u9805\u76ee\u306e\u7dcf\u6570\u3067\u3059\u3002 <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-del-calculo-de-la-proporcion-muestral\"><\/span>\u5272\u5408\u8a08\u7b97\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387\u306e\u5b9a\u7fa9\u3068\u305d\u306e\u516c\u5f0f\u3092\u7406\u89e3\u3057\u305f\u5f8c\u3001\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387\u304c\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u308b\u304b\u3092\u7406\u89e3\u3067\u304d\u308b\u3088\u3046\u306b\u7c21\u5358\u306a\u4f8b\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u3042\u308b\u4f01\u696d\u304c\u304a\u3082\u3061\u3083\u3092\u88fd\u9020\u3057\u3001\u305d\u306e\u90e8\u54c1\u306e 1 \u3064\u3092\u5225\u306e\u5916\u90e8\u4f01\u696d\u304b\u3089\u8cfc\u5165\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u8cfc\u5165\u3057\u305f\u30d0\u30c3\u30c1\u306e\u4e2d\u306b\u6b20\u9665\u90e8\u54c1\u304c\u51fa\u73fe\u3059\u308b\u305f\u3081\u3001\u72b6\u614b\u306e\u826f\u3044\u90e8\u54c1\u306e\u5272\u5408\u3068\u6b20\u9665\u306e\u5272\u5408\u3092\u8abf\u3079\u308b\u7d71\u8a08\u8abf\u67fb\u3092\u5b9f\u884c\u3059\u308b\u3053\u3068\u306b\u3057\u307e\u3057\u305f\u3002\u3057\u305f\u304c\u3063\u3066\u30011,000 \u500b\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u6ce8\u6587\u3059\u308b\u3068\u3001138 \u500b\u306e\u6b20\u9665\u90e8\u54c1\u304c\u898b\u3064\u304b\u308a\u307e\u3057\u305f\u3002\u30b5\u30f3\u30d7\u30eb\u4e2d\u306e\u826f\u597d\u306a\u72b6\u614b\u306e\u90e8\u54c1\u306e\u5272\u5408\u306f\u3069\u308c\u304f\u3089\u3044\u3067\u3059\u304b?\u307e\u305f\u3001\u30b5\u30f3\u30d7\u30eb\u4e2d\u306e\u4e0d\u826f\u54c1\u306e\u5272\u5408\u306f\u3069\u306e\u304f\u3089\u3044\u3067\u3057\u3087\u3046\u304b?<\/li>\n<\/ul>\n<p>\u30b5\u30f3\u30d7\u30eb\u5185\u306e\u640d\u50b7\u3057\u3066\u3044\u306a\u3044\u90e8\u54c1\u306e\u6570\u306f\u30011000 \u304b\u3089\u6b20\u9665\u306e\u3042\u308b\u90e8\u54c1\u306e\u6570\u3092\u5f15\u3044\u305f\u3082\u306e\u306b\u306a\u308a\u307e\u3059\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-eba1cfb3b37e9124aa6a8f3d61ba3023_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"e=1000-138=862\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"165\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u4e0a\u3067\u898b\u305f\u5f0f\u3092\u9069\u7528\u3057\u307e\u3059\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-becf48230461723d7a4d320217ad95fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}=\\cfrac{e}{n}=\\cfrac{862}{1000}=0,862\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"174\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u826f\u597d\u306a\u72b6\u614b\u306e\u90e8\u54c1\u306e\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u306f 86.2% \u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3001\u4e0d\u826f\u90e8\u54c1\u306e\u5272\u5408\u306f\u30011 \u304b\u3089\u826f\u54c1\u306e\u5272\u5408\u3092\u5f15\u3044\u305f\u3082\u306e\u3068\u7b49\u4fa1\u3067\u3059\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-14b45b7c5bc9fb8770efa40fac1f9e45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{q}=1-\\widehat{p}=1-0,862=0,138\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"237\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u6b20\u9665\u90e8\u54c1\u306e\u30b5\u30f3\u30d7\u30eb\u5272\u5408\u306f 13.8% \u306b\u306a\u308a\u307e\u3059\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"proporcion-muestral-y-proporcion-poblacional\"><\/span>\u30b5\u30f3\u30d7\u30eb\u5272\u5408\u3068\u6bcd\u96c6\u56e3\u5272\u5408<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u4eba\u53e3\u6bd4\u7387\u306f<\/strong>\u7d71\u8a08\u4e0a\u306e\u6bcd\u96c6\u56e3\u306e\u6bd4\u7387\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u6bcd\u96c6\u56e3\u306e\u5272\u5408\u306f\u3001\u6bcd\u96c6\u56e3\u306e\u4e00\u90e8\u3067\u3042\u308b\u3059\u3079\u3066\u306e\u8981\u7d20\u3068\u306e\u95a2\u9023\u3067\u8abf\u67fb\u3055\u308c\u305f\u6bcd\u96c6\u56e3\u306e\u6210\u529f\u4e8b\u4f8b\u306e\u95a2\u4fc2\u3067\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001<strong>\u56fd\u5225\u5272\u5408\u3068\u4eba\u53e3\u5272\u5408\u306e\u9055\u3044\u306f<\/strong>\u3001\u56fd\u5225\u5272\u5408\u304c\u904e\u534a\u6570\u306e\u4e8b\u4f8b\u306e\u5272\u5408\u3067\u3042\u308b\u306e\u306b\u5bfe\u3057\u3001\u4eba\u53e3\u5272\u5408\u306f\u4eba\u53e3\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u306b\u95a2\u3059\u308b\u4e8b\u8c61\u306e\u4e8b\u4f8b\u306e\u5272\u5408\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n<p>\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u3068\u6bcd\u96c6\u56e3\u306e\u5272\u5408\u3092\u533a\u5225\u3059\u308b\u305f\u3081\u306b\u3001\u305d\u308c\u3089\u306f\u7570\u306a\u308b\u8a18\u53f7\u3067\u8868\u3055\u308c\u307e\u3059\u3002\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387\u306e\u8a18\u53f7\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\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-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> \u3001\u4eba\u53e3\u6bd4\u7387\u306e\u8a18\u53f7\u306f<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u3002<\/p>\n<p>\u4e00\u822c\u306b\u3001\u3059\u3079\u3066\u306e\u6bcd\u96c6\u56e3\u306e\u5024\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u308f\u3051\u3067\u306f\u306a\u3044\u305f\u3081\u3001\u6bcd\u96c6\u56e3\u306e\u5272\u5408\u3092\u6b63\u78ba\u306b\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u4ee3\u308f\u308a\u306b\u3001\u6bcd\u96c6\u56e3\u6bd4\u7387\u306e\u5024\u306f\u901a\u5e38\u3001\u6b21\u306e\u5f0f\u306e\u4fe1\u983c\u533a\u9593\u3092\u4f7f\u7528\u3057\u3066\u63a8\u5b9a\u3055\u308c\u307e\u3059\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-6517d510181870c58b167c4d9712a7a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\left(\\widehat{p}-Z_{\\alpha\/2}\\sqrt{\\frac{\\widehat{p}(1-\\widehat{p})}{n}}\\ , \\ 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