{"id":287,"date":"2023-08-03T01:52:23","date_gmt":"2023-08-03T01:52:23","guid":{"rendered":"https:\/\/statorials.org\/hi\/z-%e0%a4%aa%e0%a4%b0%e0%a5%80%e0%a4%95%e0%a5%8d%e0%a4%b7%e0%a4%a3\/"},"modified":"2023-08-03T01:52:23","modified_gmt":"2023-08-03T01:52:23","slug":"z-%e0%a4%aa%e0%a4%b0%e0%a5%80%e0%a4%95%e0%a5%8d%e0%a4%b7%e0%a4%a3","status":"publish","type":"post","link":"https:\/\/statorials.org\/hi\/z-%e0%a4%aa%e0%a4%b0%e0%a5%80%e0%a4%95%e0%a5%8d%e0%a4%b7%e0%a4%a3\/","title":{"rendered":"\u091c\u0947\u0921 \u092a\u0930\u0940\u0915\u094d\u0937\u0923"},"content":{"rendered":"<p>\u092f\u0939 \u0906\u0932\u0947\u0916 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u092e\u0947\u0902 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u094d\u092f\u093e \u0939\u0948 \u0914\u0930 \u0907\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u0938 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f \u0906\u092a \u091c\u093e\u0928\u0947\u0902\u0917\u0947 \u0915\u093f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902, \u0935\u093f\u092d\u093f\u0928\u094d\u0928 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0938\u0942\u0924\u094d\u0930 \u0914\u0930 \u0905\u0902\u0924\u0924\u0903, Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0914\u0930 \u0905\u0928\u094d\u092f \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u092a\u0930\u0940\u0915\u094d\u0937\u0923\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0905\u0902\u0924\u0930\u0964<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-prueba-z\"><\/span>Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u094d\u092f\u093e \u0939\u0948?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0906\u0902\u0915\u0921\u093c\u094b\u0902 \u092e\u0947\u0902, <strong>Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/strong> \u090f\u0915 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0924\u092c \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0906\u0901\u0915\u0921\u093c\u0947 \u090f\u0915 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0905\u0928\u0941\u0938\u0930\u0923 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0906\u0901\u0915\u0921\u093c\u094b\u0902 \u0915\u094b Z \u0906\u0901\u0915\u0921\u093c\u093e \u092f\u093e Z \u092e\u093e\u0928 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p> Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0938\u0942\u0924\u094d\u0930 \u0939\u092e\u0947\u0936\u093e \u0938\u092e\u093e\u0928 \u0939\u094b\u0924\u093e \u0939\u0948, \u0905\u0927\u093f\u0915 \u0938\u091f\u0940\u0915 \u0930\u0942\u092a \u0938\u0947, Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0906\u0901\u0915\u0921\u093c\u093e \u0917\u0923\u0928\u093e \u0915\u093f\u090f \u0917\u090f \u0928\u092e\u0942\u0928\u093e \u092e\u0942\u0932\u094d\u092f \u0914\u0930 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u0915\u0947 \u092e\u093e\u0928\u0915 \u0935\u093f\u091a\u0932\u0928 \u0926\u094d\u0935\u093e\u0930\u093e \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u092e\u093e\u0928 \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0905\u0902\u0924\u0930 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/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 \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923\u094b\u0902 \u0915\u0940 \u0936\u0942\u0928\u094d\u092f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0915\u094b \u0905\u0938\u094d\u0935\u0940\u0915\u093e\u0930 \u0915\u0930\u0928\u0947 \u092f\u093e \u0938\u094d\u0935\u0940\u0915\u093e\u0930 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0906\u0901\u0915\u0921\u093c\u0947 \u090f\u0915 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0905\u0928\u0941\u0938\u0930\u0923 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<p> \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u092e\u093e\u0927\u094d\u092f \u0915\u0940 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0915\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u092d\u093f\u0928\u094d\u0928\u0924\u093e \u091c\u094d\u091e\u093e\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948 \u0924\u093e\u0915\u093f \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u092e\u093e\u0927\u094d\u092f \u0915\u0947 \u092e\u0942\u0932\u094d\u092f \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u090f\u0915 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0915\u094b \u0905\u0938\u094d\u0935\u0940\u0915\u093e\u0930 \u092f\u093e \u0938\u094d\u0935\u0940\u0915\u093e\u0930 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0947\u0964 <\/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>\u0926\u0947\u0916\u0947\u0902:<\/strong> <a href=\"https:\/\/statorials.org\/hi\/\u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e-\u092a\u0930\u0940\u0915\u094d\u0937\u0923-1\/\">\u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u094d\u092f\u093e \u0939\u0948?<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-pruebas-z\"><\/span> Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0947 \u092a\u094d\u0930\u0915\u093e\u0930<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u091c\u093f\u0938 \u092a\u0948\u0930\u093e\u092e\u0940\u091f\u0930 \u092a\u0930 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0909\u0938\u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923\u094b\u0902 \u0915\u094b \u0905\u0932\u0917 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u092e\u093e\u0927\u094d\u092f \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923.<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923.<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u0938\u093e\u0927\u0928\u094b\u0902 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923\u0964<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923\u0964<\/strong><\/span><\/li>\n<\/ul>\n<p> \u0928\u0940\u091a\u0947 \u0906\u092a \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0947 \u0932\u093f\u090f \u0938\u0942\u0924\u094d\u0930 \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-media\"><\/span> \u092e\u093e\u0927\u094d\u092f \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u092e\u093e\u0927\u094d\u092f \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0938\u0942\u0924\u094d\u0930<\/strong> \u0939\u0948:<\/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\"> \u0938\u094b\u0928\u093e:<\/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> \u092e\u093e\u0927\u094d\u092f \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0906\u0901\u0915\u0921\u093c\u093e \u0939\u0948\u0964<\/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> \u0928\u092e\u0942\u0928\u093e \u0938\u093e\u0927\u0928 \u0939\u0948.<\/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> \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u0914\u0938\u0924 \u092e\u0942\u0932\u094d\u092f \u0939\u0948.<\/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> \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u092e\u093e\u0928\u0915 \u0935\u093f\u091a\u0932\u0928 \u0939\u0948.<\/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> \u0928\u092e\u0942\u0928\u093e \u0906\u0915\u093e\u0930 \u0939\u0948.<\/li>\n<\/ul>\n<p> \u090f\u0915 \u092c\u093e\u0930 \u091c\u092c \u092e\u093e\u0927\u094d\u092f \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0906\u0901\u0915\u0921\u093c\u093e \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948, \u0924\u094b \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u0940 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0905\u0936\u0915\u094d\u0924 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0915\u094b \u0905\u0938\u094d\u0935\u0940\u0915\u093e\u0930 \u092f\u093e \u0905\u0938\u094d\u0935\u0940\u0915\u093e\u0930 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u0940 \u091c\u093e\u0928\u0940 \u091a\u093e\u0939\u093f\u090f:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u092f\u0926\u093f \u092e\u093e\u0927\u094d\u092f \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0926\u094b\u0924\u0930\u092b\u093e \u0939\u0948, \u0924\u094b \u092f\u0926\u093f \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u0915\u093e \u0928\u093f\u0930\u092a\u0947\u0915\u094d\u0937 \u092e\u093e\u0928 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092e\u093e\u0928 Z <sub>\u03b1\/2<\/sub> \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u0948, \u0924\u094b \u0936\u0942\u0928\u094d\u092f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0916\u093e\u0930\u093f\u091c \u0915\u0930 \u0926\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u092f\u0926\u093f \u092e\u093e\u0927\u094d\u092f \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0938\u0939\u0940 \u092a\u0942\u0902\u091b \u0938\u0947 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948, \u0924\u094b \u0936\u0942\u0928\u094d\u092f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0916\u093e\u0930\u093f\u091c \u0915\u0930 \u0926\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u092f\u0926\u093f \u0906\u0901\u0915\u0921\u093c\u093e \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092e\u093e\u0928 Z <sub>\u03b1<\/sub> \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u0948\u0964<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u092f\u0926\u093f \u092e\u093e\u0927\u094d\u092f \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u092c\u093e\u0908\u0902 \u092a\u0942\u0902\u091b \u0938\u0947 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948, \u0924\u094b \u0936\u0942\u0928\u094d\u092f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0916\u093e\u0930\u093f\u091c \u0915\u0930 \u0926\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u092f\u0926\u093f \u0906\u0901\u0915\u0921\u093c\u093e \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092e\u093e\u0928 -Z <sub>\u03b1<\/sub> \u0938\u0947 \u0915\u092e \u0939\u0948\u0964<\/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 \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0947 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092e\u093e\u0928 \u092e\u093e\u0928\u0915 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 \u0924\u093e\u0932\u093f\u0915\u093e \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 <\/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>\u0926\u0947\u0916\u0947\u0902:<\/strong> <a href=\"https:\/\/statorials.org\/hi\/\u092e\u093e\u0927\u094d\u092f-\u0915\u0947-\u0932\u093f\u090f-\u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e-\u092a\u0930\u0940\u0915\u094d\u0937\u0923\/\">\u092e\u093e\u0927\u094d\u092f \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-proporcion\"><\/span> \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0938\u0942\u0924\u094d\u0930<\/strong> \u0939\u0948:<\/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\"> \u0938\u094b\u0928\u093e:<\/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> \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0906\u0901\u0915\u0921\u093c\u093e \u0939\u0948\u0964<\/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> \u0928\u092e\u0942\u0928\u093e \u0905\u0928\u0941\u092a\u093e\u0924 \u0939\u0948.<\/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> \u092a\u094d\u0930\u0938\u094d\u0924\u093e\u0935\u093f\u0924 \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u093e \u092e\u093e\u0928 \u0939\u0948.<\/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> \u0928\u092e\u0942\u0928\u093e \u0906\u0915\u093e\u0930 \u0939\u0948.<\/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> \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u093e \u092e\u093e\u0928\u0915 \u0935\u093f\u091a\u0932\u0928 \u0939\u0948.<\/li>\n<\/ul>\n<p> \u0927\u094d\u092f\u093e\u0928 \u0930\u0916\u0947\u0902 \u0915\u093f \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0906\u0902\u0915\u0921\u093c\u094b\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u093e \u092a\u0930\u094d\u092f\u093e\u092a\u094d\u0924 \u0928\u0939\u0940\u0902 \u0939\u0948, \u092c\u0932\u094d\u0915\u093f \u0906\u092a\u0915\u094b \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u0940 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e \u0915\u0930\u0928\u0940 \u091a\u093e\u0939\u093f\u090f:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u092f\u0926\u093f \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0926\u094b\u0924\u0930\u092b\u093e \u0939\u0948, \u0924\u094b \u092f\u0926\u093f \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u0915\u093e \u092a\u0942\u0930\u094d\u0923 \u092e\u093e\u0928 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092e\u093e\u0928 Z <sub>\u03b1\/2<\/sub> \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u0948, \u0924\u094b \u0936\u0942\u0928\u094d\u092f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0916\u093e\u0930\u093f\u091c \u0915\u0930 \u0926\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948\u0964<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u092f\u0926\u093f \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0938\u0939\u0940 \u092a\u0942\u0902\u091b \u0938\u0947 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948, \u0924\u094b \u0936\u0942\u0928\u094d\u092f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0916\u093e\u0930\u093f\u091c \u0915\u0930 \u0926\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u092f\u0926\u093f \u0906\u0901\u0915\u0921\u093c\u093e \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092e\u093e\u0928 Z <sub>\u03b1<\/sub> \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u0948\u0964<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u092f\u0926\u093f \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u092c\u093e\u0908\u0902 \u092a\u0942\u0902\u091b \u0938\u0947 \u092e\u0947\u0932 \u0916\u093e\u0924\u093e \u0939\u0948, \u0924\u094b \u0936\u0942\u0928\u094d\u092f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u0916\u093e\u0930\u093f\u091c \u0915\u0930 \u0926\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948 \u092f\u0926\u093f \u0906\u0901\u0915\u0921\u093c\u093e \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092e\u093e\u0928 -Z <sub>\u03b1<\/sub> \u0938\u0947 \u0915\u092e \u0939\u0948\u0964<\/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>\u0926\u0947\u0916\u0947\u0902:<\/strong> <a href=\"https:\/\/statorials.org\/hi\/\u0905\u0928\u0941\u092a\u093e\u0924-\u0915\u0947-\u0932\u093f\u090f-\u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e-\u092a\u0930\u0940\u0915\u094d\u0937\u0923\/\">\u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-diferencia-de-medias\"><\/span> \u0938\u093e\u0927\u0928\u094b\u0902 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0938\u093e\u0927\u0928\u094b\u0902 <strong>\u092e\u0947\u0902 \u0905\u0902\u0924\u0930 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0906\u0901\u0915\u0921\u093c\u093e \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u093e \u0938\u0942\u0924\u094d\u0930<\/strong> \u0939\u0948:<\/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\"> \u0938\u094b\u0928\u093e:<\/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> \u091c\u094d\u091e\u093e\u0924 \u0935\u093f\u091a\u0930\u0923 \u0935\u093e\u0932\u0947 \u0926\u094b \u092e\u093e\u0927\u094d\u092f\u094b\u0902 \u0915\u0947 \u0905\u0902\u0924\u0930 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0906\u0901\u0915\u0921\u093c\u093e \u0939\u0948, \u091c\u094b \u090f\u0915 \u092e\u093e\u0928\u0915 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u0905\u0928\u0941\u0938\u0930\u0923 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/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> \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e 1 \u0915\u093e \u092e\u093e\u0927\u094d\u092f \u0939\u0948.<\/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> \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u092e\u093e\u0927\u094d\u092f \u0939\u0948 2.<\/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> \u0928\u092e\u0942\u0928\u093e 1 \u0915\u093e \u092e\u093e\u0927\u094d\u092f \u0939\u0948.<\/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> \u0928\u092e\u0942\u0928\u093e 2 \u0915\u093e \u092e\u093e\u0927\u094d\u092f \u0939\u0948.<\/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> \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e 1 \u0915\u093e \u092e\u093e\u0928\u0915 \u0935\u093f\u091a\u0932\u0928 \u0939\u0948.<\/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> \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e 2 \u0915\u093e \u092e\u093e\u0928\u0915 \u0935\u093f\u091a\u0932\u0928 \u0939\u0948\u0964<\/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> \u0928\u092e\u0942\u0928\u093e \u0906\u0915\u093e\u0930 1 \u0939\u0948.<\/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> \u0928\u092e\u0942\u0928\u093e \u0906\u0915\u093e\u0930 2 \u0939\u0948. <\/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>\u0926\u0947\u0916\u0947\u0902:<\/strong> <a href=\"https:\/\/statorials.org\/hi\/\u0938\u093e\u0927\u0928\u094b\u0902-\u092e\u0947\u0902-\u0905\u0902\u0924\u0930-\u0915\u0947-\u0932\u093f\u090f-\u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e-\u092a\u0930\u0940\u0915\u094d\u0937\u0923\/\">\u0938\u093e\u0927\u0928\u094b\u0902 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-diferencia-de-proporciones\"><\/span> \u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0926\u094b \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u0947 <strong>\u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0906\u0901\u0915\u0921\u093c\u093e \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u093e \u0938\u0942\u0924\u094d\u0930<\/strong> \u0939\u0948:<\/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\"> \u0938\u094b\u0928\u093e:<\/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> \u0905\u0928\u0941\u092a\u093e\u0924\u094b\u0902 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930 \u0915\u0947 \u0932\u093f\u090f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0906\u0901\u0915\u0921\u093c\u093e \u0939\u0948\u0964<\/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> \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 1 \u0939\u0948.<\/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> \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 \u0939\u0948 2.<\/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> \u0928\u092e\u0942\u0928\u093e 1 \u0915\u093e \u0905\u0928\u0941\u092a\u093e\u0924 \u0939\u0948.<\/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> \u0928\u092e\u0942\u0928\u093e \u0905\u0928\u0941\u092a\u093e\u0924 2 \u0939\u0948.<\/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> \u0928\u092e\u0942\u0928\u093e \u0906\u0915\u093e\u0930 1 \u0939\u0948.<\/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> \u0928\u092e\u0942\u0928\u093e \u0906\u0915\u093e\u0930 2 \u0939\u0948.<\/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> \u0926\u094b \u0928\u092e\u0942\u0928\u094b\u0902 \u0915\u093e \u0938\u0902\u092f\u0941\u0915\u094d\u0924 \u0905\u0928\u0941\u092a\u093e\u0924 \u0939\u0948.<\/li>\n<\/ul>\n<p> \u0926\u094b\u0928\u094b\u0902 \u0928\u092e\u0942\u0928\u094b\u0902 \u0915\u0947 \u0938\u0902\u092f\u0941\u0915\u094d\u0924 \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u0940 \u0917\u0923\u0928\u093e \u0928\u093f\u092e\u094d\u0928\u093e\u0928\u0941\u0938\u093e\u0930 \u0915\u0940 \u091c\u093e\u0924\u0940 \u0939\u0948:<\/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> \u0938\u094b\u0928\u093e<\/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> \u0928\u092e\u0942\u0928\u0947 \u092e\u0947\u0902 \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948 iy<\/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> \u0928\u092e\u0942\u0928\u093e \u0906\u0915\u093e\u0930 \u0939\u0948 I <\/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>\u0926\u0947\u0916\u0947\u0902:<\/strong> <a href=\"https:\/\/statorials.org\/hi\/\u0905\u0928\u0941\u092a\u093e\u0924-\u092e\u0947\u0902-\u0905\u0902\u0924\u0930-\u0915\u0947-\u0932\u093f\u090f-\u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e-\u092a\u0930\u0940\u0915\u094d\u0937\u0923\/\">\u0905\u0928\u0941\u092a\u093e\u0924 \u092e\u0947\u0902 \u0905\u0902\u0924\u0930 \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hacer-una-prueba-z\"><\/span>Z \u091f\u0947\u0938\u094d\u091f \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0905\u092c \u091c\u092c \u0939\u092e\u0928\u0947 \u0926\u0947\u0916 \u0932\u093f\u092f\u093e \u0939\u0948 \u0915\u093f \u0935\u093f\u092d\u093f\u0928\u094d\u0928 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0938\u0942\u0924\u094d\u0930 \u0915\u094d\u092f\u093e \u0939\u0948\u0902, \u0924\u094b \u0906\u0907\u090f \u0926\u0947\u0916\u0947\u0902 \u0915\u093f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902\u0964<\/p>\n<p> Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u091a\u0930\u0923 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 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href=\"https:\/\/statorials.org\/hi\/\u0938\u094d\u0924\u0930-\u0915\u093e-\u092e\u0939\u0924\u094d\u0935\/\">\u0905\u0932\u094d\u092b\u093e (\u03b1) \u092e\u0939\u0924\u094d\u0935 \u0938\u094d\u0924\u0930<\/a> \u092a\u0930 \u0928\u093f\u0930\u094d\u0923\u092f \u0932\u0947\u0902\u0964<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">\u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u0947\u0902 \u0915\u093f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e\u090f\u0901 \u092a\u0942\u0930\u0940 \u0915\u0940 \u0917\u0908 \u0939\u0948\u0902\u0964<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">\u0938\u0902\u0917\u0924 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0938\u0942\u0924\u094d\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0947\u0902 \u0914\u0930 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Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0914\u0930 t \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0947 \u092c\u0940\u091a \u0915\u094d\u092f\u093e \u0905\u0902\u0924\u0930 \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0935\u0947 \u0928\u093f\u0936\u094d\u091a\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u0906\u0902\u0915\u0921\u093c\u094b\u0902 \u092e\u0947\u0902 \u0938\u092c\u0938\u0947 \u0905\u0927\u093f\u0915 \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u090f \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0947 \u0926\u094b \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0939\u0948\u0902\u0964<\/p>\n<p> <strong>\u091f\u0940-\u091f\u0947\u0938\u094d\u091f<\/strong> , \u091c\u093f\u0938\u0947 <strong>\u091b\u093e\u0924\u094d\u0930 \u0915\u093e \u091f\u0940-\u091f\u0947\u0938\u094d\u091f<\/strong> \u092d\u0940 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u090f\u0915 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0924\u092c \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0940 \u091c\u093e \u0930\u0939\u0940 \u0906\u092c\u093e\u0926\u0940 \u0938\u093e\u092e\u093e\u0928\u094d\u092f \u0935\u093f\u0924\u0930\u0923 \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930\u0924\u0940 \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u092d\u093f\u0928\u094d\u0928\u0924\u093e \u091c\u093e\u0928\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0928\u092e\u0942\u0928\u093e \u0906\u0915\u093e\u0930 \u092c\u0939\u0941\u0924 \u091b\u094b\u091f\u093e \u0939\u0948\u0964<\/p>\n<p> \u0907\u0938\u0932\u093f\u090f, <strong>Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0914\u0930 t \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u0947 \u0915\u0947 \u092c\u0940\u091a \u092e\u0941\u0916\u094d\u092f \u0905\u0902\u0924\u0930<\/strong> \u092f\u0939 \u0939\u0948 \u0915\u093f \u092d\u093f\u0928\u094d\u0928\u0924\u093e \u091c\u094d\u091e\u093e\u0924 \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902\u0964 \u091c\u092c \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u092d\u093f\u0928\u094d\u0928\u0924\u093e \u091c\u094d\u091e\u093e\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0924\u094b Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u091c\u092c\u0915\u093f \u091c\u092c \u091c\u0928\u0938\u0902\u0916\u094d\u092f\u093e \u092d\u093f\u0928\u094d\u0928\u0924\u093e \u0905\u091c\u094d\u091e\u093e\u0924 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0924\u094b t \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 <\/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>\u0926\u0947\u0916\u0947\u0902:<\/strong> <a href=\"https:\/\/statorials.org\/hi\/\u091b\u093e\u0924\u094d\u0930-\u091f\u0940-\u091f\u0947\u0938\u094d\u091f\/\">\u091f\u0940 \u092a\u0930\u0940\u0915\u094d\u0937\u0923 (\u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940)<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u092f\u0939 \u0906\u0932\u0947\u0916 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u092e\u0947\u0902 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u094d\u092f\u093e \u0939\u0948 \u0914\u0930 \u0907\u0938\u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u0938 \u0932\u093f\u090f \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f \u0906\u092a \u091c\u093e\u0928\u0947\u0902\u0917\u0947 \u0915\u093f Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902, \u0935\u093f\u092d\u093f\u0928\u094d\u0928 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0938\u0942\u0924\u094d\u0930 \u0914\u0930 \u0905\u0902\u0924\u0924\u0903, Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0914\u0930 \u0905\u0928\u094d\u092f \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u092a\u0930\u0940\u0915\u094d\u0937\u0923\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0905\u0902\u0924\u0930\u0964 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u094d\u092f\u093e \u0939\u0948? \u0906\u0902\u0915\u0921\u093c\u094b\u0902 \u092e\u0947\u0902, Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u090f\u0915 \u092a\u0930\u093f\u0915\u0932\u094d\u092a\u0928\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0939\u0948 \u091c\u093f\u0938\u0915\u093e [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"class_list":["post-287","post","type-post","status-publish","format-standard","hentry","category-6"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7Z-\u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/title>\n<meta name=\"description\" content=\"\u092f\u0939\u093e\u0902 \u0906\u092a \u091c\u093e\u0928\u0947\u0902\u0917\u0947 \u0915\u093f \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u092e\u0947\u0902 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u094d\u092f\u093e \u0939\u0948, Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902 (\u0938\u0942\u0924\u094d\u0930) \u0914\u0930 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0947 \u0939\u0932 \u0915\u093f\u090f \u0917\u090f \u0909\u0926\u093e\u0939\u0930\u0923\u0964\" \/>\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\/hi\/z-\u092a\u0930\u0940\u0915\u094d\u0937\u0923\/\" \/>\n<meta property=\"og:locale\" content=\"hi_IN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7Z-\u092a\u0930\u0940\u0915\u094d\u0937\u0923\" \/>\n<meta property=\"og:description\" content=\"\u092f\u0939\u093e\u0902 \u0906\u092a \u091c\u093e\u0928\u0947\u0902\u0917\u0947 \u0915\u093f \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940 \u092e\u0947\u0902 Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u094d\u092f\u093e \u0939\u0948, Z \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0948\u0938\u0947 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