{"id":259,"date":"2023-08-03T11:07:43","date_gmt":"2023-08-03T11:07:43","guid":{"rendered":"https:\/\/statorials.org\/ja\/%e5%89%b2%e5%90%88%e3%81%ae%e4%bb%ae%e8%aa%ac%e6%a4%9c%e5%ae%9a\/"},"modified":"2023-08-03T11:07:43","modified_gmt":"2023-08-03T11:07:43","slug":"%e5%89%b2%e5%90%88%e3%81%ae%e4%bb%ae%e8%aa%ac%e6%a4%9c%e5%ae%9a","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/%e5%89%b2%e5%90%88%e3%81%ae%e4%bb%ae%e8%aa%ac%e6%a4%9c%e5%ae%9a\/","title":{"rendered":"\u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7d71\u8a08\u5b66\u306b\u304a\u3051\u308b\u4eee\u8aac\u691c\u5b9a\u306e\u5272\u5408\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a\u306e\u516c\u5f0f\u3068\u3001\u305d\u306e\u65b9\u6cd5\u3092\u5b8c\u5168\u306b\u7406\u89e3\u3059\u308b\u305f\u3081\u306e\u6bb5\u968e\u7684\u306a\u6f14\u7fd2\u304c\u898b\u3064\u304b\u308a\u307e\u3059\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>\u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>\u6bd4\u7387\u4eee\u8aac\u691c\u5b9a\u306f<\/strong>\u3001\u6bcd\u96c6\u56e3\u6bd4\u7387\u306e\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u6c7a\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u7d71\u8a08\u624b\u6cd5\u3067\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u5272\u5408\u3068\u6709\u610f\u6c34\u6e96\u306e\u4eee\u8aac\u691c\u5b9a\u7d71\u8a08\u91cf\u306e\u5024\u306b\u5fdc\u3058\u3066\u3001\u5e30\u7121\u4eee\u8aac\u306f\u68c4\u5374\u3055\u308c\u308b\u304b\u53d7\u3051\u5165\u308c\u3089\u308c\u307e\u3059\u3002<\/p>\n<p>\u4eee\u8aac\u691c\u5b9a\u306f\u3001\u4eee\u8aac\u5bfe\u6bd4\u3001\u4eee\u8aac\u691c\u5b9a\u3001\u307e\u305f\u306f\u6709\u610f\u6027\u691c\u5b9a\u3068\u3082\u547c\u3070\u308c\u308b\u3053\u3068\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002 <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-prueba-de-hipotesis-para-la-proporcion\"><\/span>\u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a\u516c\u5f0f<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a\u7d71\u8a08\u91cf\u306f\u3001\u30b5\u30f3\u30d7\u30eb\u5272\u5408\u306e\u5dee\u304b\u3089\u5272\u5408\u306e\u63d0\u6848\u5024\u3092\u5f15\u3044\u305f\u3082\u306e\u3092\u5272\u5408\u306e\u6a19\u6e96\u504f\u5dee\u3067\u5272\u3063\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066<strong>\u3001\u6bd4\u7387\u306e\u691c\u5b9a\u4eee\u8aac\u306e\u5f0f\u306f<\/strong>\u6b21\u306e\u3088\u3046\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-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\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>\u306f\u3001\u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a\u7d71\u8a08\u91cf\u3067\u3059\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>\u306f\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u3067\u3059\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>\u63d0\u6848\u3055\u308c\u305f\u6bd4\u7387\u306e\u5024\u3067\u3059\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>\u306f\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u3067\u3059\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>\u306f\u6bd4\u7387\u306e\u6a19\u6e96\u504f\u5dee\u3067\u3059\u3002<\/li>\n<\/ul>\n<p>\u6bd4\u7387\u306e\u4eee\u8aac\u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u8a08\u7b97\u3059\u308b\u3060\u3051\u3067\u306f\u5341\u5206\u3067\u306f\u306a\u304f\u3001\u7d50\u679c\u3092\u89e3\u91c8\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u6bd4\u7387\u306e\u4eee\u8aac\u691c\u5b9a\u304c\u4e21\u5074\u3067\u3042\u308b\u5834\u5408\u3001\u7d71\u8a08\u91cf\u306e\u7d76\u5bfe\u5024\u304c\u81e8\u754c\u5024 Z <sub>\u03b1\/2<\/sub>\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u5e30\u7121\u4eee\u8aac\u306f\u68c4\u5374\u3055\u308c\u307e\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u6bd4\u7387\u306e\u4eee\u8aac\u691c\u5b9a\u304c\u53f3\u88fe\u306b\u4e00\u81f4\u3059\u308b\u5834\u5408\u3001\u7d71\u8a08\u91cf\u304c\u81e8\u754c\u5024 Z <sub>\u03b1<\/sub>\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u5e30\u7121\u4eee\u8aac\u306f\u68c4\u5374\u3055\u308c\u307e\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a\u304c\u5de6\u88fe\u306b\u4e00\u81f4\u3059\u308b\u5834\u5408\u3001\u7d71\u8a08\u91cf\u304c\u81e8\u754c\u5024 -Z <sub>\u03b1<\/sub>\u3088\u308a\u5c0f\u3055\u3044\u5834\u5408\u3001\u5e30\u7121\u4eee\u8aac\u306f\u68c4\u5374\u3055\u308c\u307e\u3059\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>\u81e8\u754c\u5024\u306f\u6b63\u898f\u5206\u5e03\u8868\u304b\u3089\u7c21\u5358\u306b\u53d6\u5f97\u3067\u304d\u308b\u3053\u3068\u3092\u899a\u3048\u3066\u304a\u3044\u3066\u304f\u3060\u3055\u3044\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\/\u6b63\u898f\u5206\u5e03\u8868\/\">\u6b63\u898f\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>\u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a\u306e\u4f8b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6bd4\u7387\u306e\u4eee\u8aac\u691c\u5b9a\u306e\u5b9a\u7fa9\u3068\u305d\u306e\u5f0f\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u7406\u89e3\u3057\u305f\u3089\u3001\u6982\u5ff5\u3092\u3088\u308a\u3088\u304f\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u4f8b\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\u30e1\u30fc\u30ab\u30fc\u306b\u3088\u308c\u3070\u3001\u7279\u5b9a\u306e\u75c5\u6c17\u306b\u5bfe\u3059\u308b\u85ac\u306e\u6709\u52b9\u7387\u306f 70% \u3067\u3059\u3002\u7814\u7a76\u8005\u306f\u5272\u5408\u304c\u7570\u306a\u308b\u3068\u4fe1\u3058\u3066\u3044\u308b\u305f\u3081\u3001\u7814\u7a76\u5ba4\u3067\u306f\u3053\u306e\u85ac\u306e\u6709\u52b9\u6027\u3092\u30c6\u30b9\u30c8\u3057\u307e\u3059\u3002\u3053\u306e\u305f\u3081\u3001\u3053\u306e\u85ac\u306f1,000\u4eba\u306e\u60a3\u8005\u306e\u30b5\u30f3\u30d7\u30eb\u3067\u8a66\u9a13\u3055\u308c\u3001641\u4eba\u304c\u6cbb\u7652\u3057\u305f\u3002\u7814\u7a76\u8005\u306e\u4eee\u8aac\u3092\u68c4\u5374\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u6c7a\u5b9a\u3059\u308b\u305f\u3081\u306b\u3001\u6709\u610f\u6c34\u6e96 5% \u3067\u6bcd\u96c6\u56e3\u306e\u5272\u5408\u306b\u5bfe\u3057\u3066\u4eee\u8aac\u691c\u5b9a\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002<\/li>\n<\/ul>\n<p>\u3053\u306e\u5834\u5408\u3001\u6bcd\u96c6\u56e3\u306e\u5272\u5408\u306b\u5bfe\u3059\u308b\u4eee\u8aac\u691c\u5b9a\u306e<a href=\"https:\/\/statorials.org\/ja\/\u5e30\u7121\u4eee\u8aac\u3068\u5bfe\u7acb\u4eee\u8aac\/\">\u5e30\u7121\u4eee\u8aac\u3068\u5bfe\u7acb\u4eee\u8aac\u306f<\/a>\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-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>\u30b5\u30f3\u30d7\u30eb\u306b\u542b\u307e\u308c\u308b\u3053\u306e\u85ac\u306b\u3088\u3063\u3066\u6cbb\u7652\u3057\u305f\u4eba\u306e\u5272\u5408\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-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>\u4e0a\u8a18\u306e\u5f0f\u3092\u9069\u7528\u3057\u3066\u3001\u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u8a08\u7b97\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-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>\u4e00\u65b9\u3001\u6709\u610f\u6c34\u6e96\u306f 0.05 \u3067\u3042\u308a\u3001\u3053\u308c\u306f\u4e21\u5074\u4eee\u8aac\u691c\u5b9a\u3067\u3042\u308b\u305f\u3081\u3001\u691c\u5b9a\u306e\u81e8\u754c\u5024\u306f 1.96 \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-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>\u53c2\u7167:<\/strong><a href=\"https:\/\/statorials.org\/ja\/\u91cd\u8981\u6027\u306e\u30ec\u30d8\u3099\u30eb\/\">\u6709\u610f\u6c34\u6e96 0.05<\/a><\/div>\n<p>\u7d50\u8ad6\u3068\u3057\u3066\u3001\u691c\u5b9a\u7d71\u8a08\u91cf\u306e\u7d76\u5bfe\u5024\u306f\u81e8\u754c\u5024\u3088\u308a\u5927\u304d\u3044\u305f\u3081\u3001\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u3057\u3001\u5bfe\u7acb\u4eee\u8aac\u3092\u53d7\u3051\u5165\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-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>\u53c2\u7167:<\/strong><a href=\"https:\/\/statorials.org\/ja\/\u5e73\u5747\u306b\u5bfe\u3059\u308b\u4eee\u8aac\u691c\u5b9a\/\">\u5e73\u5747\u5024\u306e\u4eee\u8aac\u691c\u5b9a<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-de-hipotesis-para-las-proporciones-de-dos-muestras\"><\/span> 2 \u3064\u306e\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387\u306b\u5bfe\u3059\u308b\u4eee\u8aac\u691c\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>2 \u3064\u306e\u30b5\u30f3\u30d7\u30eb\u306e\u6bd4\u7387\u306b\u95a2\u3059\u308b\u4eee\u8aac\u691c\u5b9a\u306f\u3001<\/strong> 2 \u3064\u306e\u7570\u306a\u308b\u6bcd\u96c6\u56e3\u306e\u6bd4\u7387\u304c\u7b49\u3057\u3044\u3068\u3044\u3046\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u307e\u305f\u306f\u53d7\u3051\u5165\u308c\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>\n<p>\u3057\u305f\u304c\u3063\u3066\u30012 \u30b5\u30f3\u30d7\u30eb\u306e\u6bd4\u7387\u306b\u5bfe\u3059\u308b\u4eee\u8aac\u691c\u5b9a\u306e\u5e30\u7121\u4eee\u8aac\u306f\u5e38\u306b\u6b21\u306e\u3088\u3046\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-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>\u4e00\u65b9\u3001\u5bfe\u7acb\u4eee\u8aac\u306f\u6b21\u306e 3 \u3064\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u306e\u3044\u305a\u308c\u304b\u306b\u306a\u308a\u307e\u3059\u3002<\/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> 2 \u3064\u306e\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387\u306b\u5bfe\u3059\u308b\u4eee\u8aac\u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u8a08\u7b97\u3059\u308b\u5f0f\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-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\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>\u306f\u30012 \u3064\u306e\u6a19\u672c\u6bd4\u7387\u306e\u4eee\u8aac\u691c\u5b9a\u7d71\u8a08\u91cf\u3067\u3059\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>\u306f\u30b5\u30f3\u30d7\u30eb 1 \u306e\u7d50\u679c\u306e\u6570\u3067\u3059\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>\u306f\u30b5\u30f3\u30d7\u30eb 2 \u306e\u7d50\u679c\u306e\u6570\u3067\u3059\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>\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f1\u3067\u3059\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>\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306f2\u3067\u3059\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>\u306f 2 \u3064\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u5408\u308f\u305b\u305f\u6bd4\u7387\u3067\u3059\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 \u500b\u306e\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387\u306b\u5bfe\u3059\u308b\u4eee\u8aac\u691c\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>k \u500b\u306e\u30b5\u30f3\u30d7\u30eb\u306e\u5272\u5408\u306b\u95a2\u3059\u308b\u4eee\u8aac\u691c\u5b9a\u306e\u76ee\u7684\u306f\u3001<\/strong>\u7570\u306a\u308b\u6bcd\u96c6\u56e3\u306e\u5272\u5408\u304c\u3059\u3079\u3066\u7b49\u3057\u3044\u304b\u3069\u3046\u304b\u3001\u3042\u308b\u3044\u306f\u9006\u306b\u7570\u306a\u308b\u5272\u5408\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u5834\u5408\u306e\u5e30\u7121\u4eee\u8aac\u3068\u5bfe\u7acb\u4eee\u8aac\u306f\u6b21\u306e\u3088\u3046\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-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>\u3053\u306e\u5834\u5408\u3001\u3059\u3079\u3066\u306e\u30b5\u30f3\u30d7\u30eb\u306e\u5408\u8a08\u6bd4\u7387\u306f\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\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-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> k \u500b\u306e\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387\u306b\u5bfe\u3059\u308b\u4eee\u8aac\u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u6c42\u3081\u308b\u5f0f\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-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\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>\u306f\u3001k \u500b\u306e\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387\u306b\u5bfe\u3059\u308b\u4eee\u8aac\u691c\u5b9a\u7d71\u8a08\u91cf\u3067\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u7d71\u8a08\u306f\u30ab\u30a4\u4e8c\u4e57\u5206\u5e03\u306b\u5f93\u3044\u307e\u3059\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>\u30b5\u30f3\u30d7\u30eb i \u306e\u7d50\u679c\u306e\u6570\u3067\u3059\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>\u306f\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba i \u3067\u3059\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>\u3059\u3079\u3066\u306e\u30b5\u30f3\u30d7\u30eb\u306e\u5408\u8a08\u306e\u5272\u5408\u3067\u3059\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>\u306f\u30b5\u30f3\u30d7\u30eb i \u304b\u3089\u4e88\u60f3\u3055\u308c\u308b\u30d2\u30c3\u30c8\u6570\u3067\u3059\u3002\u7d44\u307f\u5408\u308f\u305b\u305f\u6bd4\u7387\u3092\u4e57\u3058\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059<\/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>\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba\u306b\u3088\u308b<\/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>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7d71\u8a08\u5b66\u306b\u304a\u3051\u308b\u4eee\u8aac\u691c\u5b9a\u306e\u5272\u5408\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a\u306e\u516c\u5f0f\u3068\u3001\u305d\u306e\u65b9\u6cd5\u3092\u5b8c\u5168\u306b\u7406\u89e3\u3059\u308b\u305f\u3081\u306e\u6bb5\u968e\u7684\u306a\u6f14\u7fd2\u304c\u898b\u3064\u304b\u308a\u307e\u3059\u3002 \u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a\u3068\u306f\u4f55\u3067\u3059\u304b? \u6bd4\u7387\u4eee\u8aac\u691c\u5b9a\u306f\u3001\u6bcd\u96c6\u56e3\u6bd4\u7387\u306e\u5e30\u7121 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