{"id":286,"date":"2023-08-03T01:52:23","date_gmt":"2023-08-03T01:52:23","guid":{"rendered":"https:\/\/statorials.org\/ja\/z-%e6%a4%9c%e5%ae%9a\/"},"modified":"2023-08-03T01:52:23","modified_gmt":"2023-08-03T01:52:23","slug":"z-%e6%a4%9c%e5%ae%9a","status":"publish","type":"post","link":"https:\/\/statorials.org\/ja\/z-%e6%a4%9c%e5%ae%9a\/","title":{"rendered":"Z \u691c\u5b9a"},"content":{"rendered":"<p>\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u7d71\u8a08\u306b\u304a\u3051\u308b Z \u691c\u5b9a\u3068\u306f\u4f55\u304b\u3001\u307e\u305f\u305d\u306e\u7528\u9014\u306b\u3064\u3044\u3066\u8aac\u660e\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001Z \u691c\u5b9a\u306e\u5b9f\u884c\u65b9\u6cd5\u3001\u3055\u307e\u3056\u307e\u306a Z \u691c\u5b9a\u306e\u516c\u5f0f\u3001\u305d\u3057\u3066\u6700\u5f8c\u306b\u3001Z \u691c\u5b9a\u3068\u4ed6\u306e\u7d71\u8a08\u691c\u5b9a\u306e\u9055\u3044\u3092\u7406\u89e3\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-prueba-z\"><\/span>Z \u30c6\u30b9\u30c8\u3068\u306f\u4f55\u3067\u3059\u304b?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7d71\u8a08\u5b66\u306b\u304a\u3051\u308b<strong>Z \u691c\u5b9a\u306f<\/strong>\u3001\u691c\u5b9a\u7d71\u8a08\u91cf\u304c\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u5834\u5408\u306b\u4f7f\u7528\u3055\u308c\u308b\u4eee\u8aac\u691c\u5b9a\u3067\u3059\u3002 Z \u691c\u5b9a\u304b\u3089\u5f97\u3089\u308c\u308b\u7d71\u8a08\u91cf\u306f\u3001Z \u7d71\u8a08\u91cf\u307e\u305f\u306f Z \u5024\u3068\u547c\u3070\u308c\u307e\u3059\u3002<\/p>\n<p> Z \u691c\u5b9a\u306e\u5f0f\u306f\u5e38\u306b\u540c\u3058\u3067\u3059\u3002\u3088\u308a\u6b63\u78ba\u306b\u306f\u3001Z \u691c\u5b9a\u306e\u7d71\u8a08\u91cf\u306f\u3001\u8a08\u7b97\u3055\u308c\u305f\u30b5\u30f3\u30d7\u30eb\u5024\u3068\u63d0\u6848\u3055\u308c\u305f\u6bcd\u96c6\u56e3\u306e\u5024\u306e\u5dee\u3092\u6bcd\u96c6\u56e3\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306e\u6a19\u6e96\u504f\u5dee\u3067\u5272\u3063\u305f\u3082\u306e\u306b\u7b49\u3057\u304f\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-5ad1fab5e2c6a8d32ae02f2e2d16d42c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\widehat{X}-X}{\\sigma_{_X}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"92\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Z \u691c\u5b9a\u306f\u3001\u691c\u5b9a\u7d71\u8a08\u91cf\u304c\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u4eee\u8aac\u691c\u5b9a\u306e\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>\u305f\u3068\u3048\u3070\u3001Z \u691c\u5b9a\u306f\u3001\u6bcd\u96c6\u56e3\u306e\u5206\u6563\u304c\u308f\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u306b\u3001\u6bcd\u96c6\u56e3\u306e\u5e73\u5747\u5024\u306b\u95a2\u3059\u308b\u4eee\u8aac\u3092\u68c4\u5374\u307e\u305f\u306f\u53d7\u3051\u5165\u308c\u308b\u305f\u3081\u306b\u3001\u5e73\u5747\u306e\u4eee\u8aac\u3092\u691c\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\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\/\u4eee\u8aac\u691c\u8a3c1\/\">\u4eee\u8aac\u691c\u5b9a\u3068\u306f\u4f55\u3067\u3059\u304b?<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-pruebas-z\"><\/span> Z \u30c6\u30b9\u30c8\u306e\u7a2e\u985e<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u4eee\u8aac\u691c\u5b9a\u304c\u5b9f\u884c\u3055\u308c\u308b\u30d1\u30e9\u30e1\u30fc\u30bf\u30fc\u306b\u5fdc\u3058\u3066\u3001\u3055\u307e\u3056\u307e\u306a\u30bf\u30a4\u30d7\u306e Z \u691c\u5b9a\u3092\u533a\u5225\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u5e73\u5747\u5024\u306e Z \u691c\u5b9a\u3002<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u6bd4\u7387\u306e Z \u691c\u5b9a\u3002<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u5e73\u5747\u306e\u5dee\u306e Z \u691c\u5b9a\u3002<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\"><strong>\u6bd4\u7387\u306e\u5dee\u306b\u3064\u3044\u3066\u306e Z \u691c\u5b9a\u3002<\/strong><\/span><\/li>\n<\/ul>\n<p>\u4ee5\u4e0b\u306b\u3001Z \u30c6\u30b9\u30c8\u306e\u5404\u30bf\u30a4\u30d7\u306e\u5f0f\u3092\u793a\u3057\u307e\u3059\u3002<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-media\"><\/span>\u5e73\u5747\u5024\u306e Z \u691c\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u5e73\u5747\u5024\u306e Z \u691c\u5b9a\u5f0f\u306f\u6b21\u306e<\/strong>\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-fdf1817a07bfb8c1eda9a8d8ccd8c828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{\\sigma}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"81\" style=\"vertical-align: -34px;\"><\/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\u5e73\u5747\u5024\u306e Z \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-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>\u306f\u30b5\u30f3\u30d7\u30eb\u5e73\u5747\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-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>\u306f\u63d0\u6848\u3055\u308c\u305f\u5e73\u5747\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-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>\u306f\u6bcd\u96c6\u56e3\u306e\u6a19\u6e96\u504f\u5dee\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<\/ul>\n<p>\u5e73\u5747\u306e\u4eee\u8aac\u691c\u5b9a\u7d71\u8a08\u91cf\u304c\u8a08\u7b97\u3055\u308c\u308b\u3068\u3001\u305d\u306e\u7d50\u679c\u306f\u5e30\u7121\u4eee\u8aac\u3092\u68c4\u5374\u307e\u305f\u306f\u68c4\u5374\u3059\u308b\u3068\u89e3\u91c8\u3055\u308c\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"><span style=\"color:#101010;font-weight: normal;\">\u5e73\u5747\u5024\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;\">\u5e73\u5747\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;\">\u5e73\u5747\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-0e2ccadfc369eb7543b8f86dfccc528e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: \\mu\\neq \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |Z|>Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_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=\"440\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Z \u691c\u5b9a\u306e\u81e8\u754c\u5024\u306f\u6a19\u6e96\u6b63\u898f\u5206\u5e03\u8868\u304b\u3089\u5f97\u3089\u308c\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\/\u5e73\u5747\u306b\u5bfe\u3059\u308b\u4eee\u8aac\u691c\u5b9a\/\">\u5e73\u5747\u5024\u306e\u4eee\u8aac\u691c\u5b9a<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-proporcion\"><\/span>\u6bd4\u7387\u306e Z \u691c\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u6bd4\u7387\u306e Z \u691c\u5b9a\u5f0f\u306f\u6b21<\/strong>\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-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\u5272\u5408\u306e Z \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 Z \u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u8a08\u7b97\u3059\u308b\u3060\u3051\u3067\u306f\u5341\u5206\u3067\u306f\u306a\u304f\u3001\u5f97\u3089\u308c\u305f\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<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\/\u5272\u5408\u306e\u4eee\u8aac\u691c\u5b9a\/\">\u6bd4\u7387\u306e\u4eee\u8aac\u691c\u5b9a<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-diferencia-de-medias\"><\/span>\u5e73\u5747\u5024\u306e\u5dee\u306e Z \u691c\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>\u5e73\u5747\u306e\u5dee\u306e Z \u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u8a08\u7b97\u3059\u308b\u5f0f\u306f\u6b21<\/strong>\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-0b7968d96046c1f555a7c95e7c3c408e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\displaystyle (\\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=\"78\" width=\"203\" 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\u3001\u65e2\u77e5\u306e\u5206\u6563\u3092\u6301\u3064 2 \u3064\u306e\u5e73\u5747\u306e\u5dee\u306e Z \u691c\u5b9a\u7d71\u8a08\u91cf\u3067\u3042\u308a\u3001\u6a19\u6e96\u6b63\u898f\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-776e8d37515f607d16b6ea33cf27cb8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u306f\u6bcd\u96c6\u56e3 1 \u306e\u5e73\u5747\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-eed6e51baac07f2aaf1c82b4b328ded8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u306f\u6bcd\u96c6\u56e3 2 \u306e\u5e73\u5747\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-1436bb55d331d1efe559fd1e55245851_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u306f\u30b5\u30f3\u30d7\u30eb 1 \u306e\u5e73\u5747\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-f06b28a75570ecb4df1371dea2d9f2b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u306f\u30b5\u30f3\u30d7\u30eb 2 \u306e\u5e73\u5747\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-802bfc799b8f222d7b47270e1569770b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u306f\u6bcd\u96c6\u56e3 1 \u306e\u6a19\u6e96\u504f\u5dee\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-063ad2fadbc81bd1df35589566b0bd16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"><\/p>\n<p>\u306f\u6bcd\u96c6\u56e3 2 \u306e\u6a19\u6e96\u504f\u5dee\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<\/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>\u53c2\u7167:<\/strong><a href=\"https:\/\/statorials.org\/ja\/\u5e73\u5747\u306e\u5dee\u306e\u4eee\u8aac\u691c\u5b9a\/\">\u5e73\u5747\u306e\u5dee\u306e\u4eee\u8aac\u691c\u5b9a<\/a><\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-diferencia-de-proporciones\"><\/span>\u6bd4\u7387\u306e\u5dee\u306e Z \u691c\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>2 \u3064\u306e\u6bcd\u96c6\u56e3\u306e<strong>\u6bd4\u7387\u306e\u5dee\u306b\u95a2\u3059\u308b Z \u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u8a08\u7b97\u3059\u308b\u5f0f\u306f\u6b21\u306e<\/strong>\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-161267e1562535b8ded23017389e0807_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\displaystyle (\\widehat{p_1}-\\widehat{p_2})-(p_1-p_2)}{\\displaystyle \\sqrt{p_0(1-p_0)\\left(\\frac{1}{n_1}+\\frac{1}{n_2}\\right)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"229\" 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\u3001\u6bd4\u7387\u306e\u5dee\u3092\u8868\u3059 Z \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-023bcfb3fa329ff4f481163d36b65bf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u306f\u4eba\u53e3 1 \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-1a0ac2d00900c29ac35c13956874c642_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u306f\u4eba\u53e32\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-a4c76b176c372799a3a3a7aa8858eecf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u306f\u30b5\u30f3\u30d7\u30eb 1 \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-cd7916af5298a603fad64ab8fb2501a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p>\u30b5\u30f3\u30d7\u30eb\u6bd4\u7387 2 \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-ccd892ed2f60029f47331cf785d30482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" 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<p> 2 \u3064\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-6f349422474d622468a6a14f445f2eb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_0=\\cfrac{x_1+x_2}{n_1+n_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"102\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p>\u91d1<\/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-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 iy \u5185\u306e\u7d50\u679c\u306e\u6570\u3067\u3059\u3002<\/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>\u306f\u30b5\u30f3\u30d7\u30eb\u30b5\u30a4\u30ba i \u3067\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\/\u6bd4\u7387\u306e\u9055\u3044\u306b\u95a2\u3059\u308b\u4eee\u8aac\u691c\u5b9a\/\">\u6bd4\u7387\u306e\u9055\u3044\u306b\u95a2\u3059\u308b\u4eee\u8aac\u691c\u5b9a<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hacer-una-prueba-z\"><\/span>Z \u30c6\u30b9\u30c8\u306e\u3084\u308a\u65b9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u3055\u307e\u3056\u307e\u306a Z \u30c6\u30b9\u30c8\u306e\u516c\u5f0f\u304c\u4f55\u3067\u3042\u308b\u304b\u3092\u7406\u89e3\u3057\u305f\u306e\u3067\u3001\u6b21\u306f Z 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style=\"color:#101010;font-weight: normal;\">Z \u30c6\u30b9\u30c8\u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u306e\u8981\u4ef6\u304c\u6e80\u305f\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"><span style=\"color:#101010;font-weight: normal;\">\u5bfe\u5fdc\u3059\u308b Z \u691c\u5b9a\u5f0f\u3092\u9069\u7528\u3057\u3001\u691c\u5b9a\u7d71\u8a08\u91cf\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Z \u30c6\u30b9\u30c8\u306e\u7d50\u679c\u3092\u81e8\u754c\u30c6\u30b9\u30c8\u5024\u3068\u6bd4\u8f03\u3057\u3066\u89e3\u91c8\u3057\u307e\u3059\u3002<\/span><\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-y-prueba-t\"><\/span>Z \u691c\u5b9a\u3068 t \u691c\u5b9a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6700\u5f8c\u306b\u3001Z \u691c\u5b9a\u3068 t 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