{"id":259,"date":"2023-08-03T11:26:47","date_gmt":"2023-08-03T11:26:47","guid":{"rendered":"https:\/\/statorials.org\/my\/%e1%80%86%e1%80%ad%e1%80%af%e1%80%9c%e1%80%ad%e1%80%af%e1%80%9b%e1%80%84%e1%80%ba%e1%80%b8%e1%80%a1%e1%80%90%e1%80%bd%e1%80%80%e1%80%ba-hypothesis-test\/"},"modified":"2023-08-03T11:26:47","modified_gmt":"2023-08-03T11:26:47","slug":"%e1%80%86%e1%80%ad%e1%80%af%e1%80%9c%e1%80%ad%e1%80%af%e1%80%9b%e1%80%84%e1%80%ba%e1%80%b8%e1%80%a1%e1%80%90%e1%80%bd%e1%80%80%e1%80%ba-hypothesis-test","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/%e1%80%86%e1%80%ad%e1%80%af%e1%80%9c%e1%80%ad%e1%80%af%e1%80%9b%e1%80%84%e1%80%ba%e1%80%b8%e1%80%a1%e1%80%90%e1%80%bd%e1%80%80%e1%80%ba-hypothesis-test\/","title":{"rendered":"\u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u101a\u1030\u1006\u1001\u103b\u1000\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u104b"},"content":{"rendered":"<p>\u1024\u1006\u1031\u102c\u1004\u103a\u1038\u1015\u102b\u1038\u101e\u100a\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1006\u102d\u102f\u101c\u102d\u102f\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u1019\u100a\u103a\u1000\u1032\u1037\u101e\u102d\u102f\u1037\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u1021\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u101e\u1004\u103a\u101e\u100a\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1010\u103d\u1000\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u1010\u103d\u1031\u1037\u101b\u1019\u100a\u103a\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038\u104a \u1011\u102d\u102f\u1037\u1021\u1015\u103c\u1004\u103a \u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u1001\u1014\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1015\u103c\u102e\u1038\u1010\u1005\u103a\u1001\u102f \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a\u1016\u103c\u1031\u101b\u103e\u1004\u103a\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-prueba-de-hipotesis-para-la-media\"><\/span> \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a hypothesis testing \u1006\u102d\u102f\u1010\u102c \u1018\u102c\u101c\u1032\u104b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1010\u103d\u1000\u103a \u1010\u103d\u1031\u1038\u1001\u1031\u102b\u103a\u1019\u103e\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038<\/strong> \u101e\u100a\u103a \u101c\u1030\u1026\u1038\u101b\u1031\u1006\u102d\u102f\u101c\u102d\u102f\u1001\u103b\u1000\u103a\u104f null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/p>\n<p> \u1015\u102d\u102f\u104d\u1010\u102d\u1000\u103b\u101e\u100a\u103a\u1019\u103e\u102c\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u1010\u103d\u1004\u103a \u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u1014\u103e\u1004\u1037\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1001\u103c\u1004\u103a\u1038 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1019\u1004\u103c\u1004\u103a\u1038\u101b\u1014\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1014\u103e\u1004\u1037\u103a \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1001\u103c\u1004\u103a\u1038\u1010\u102d\u102f\u1037 \u1015\u102b\u101d\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/p>\n<p> \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u1019\u100a\u103a\u1021\u1019\u103b\u102d\u102f\u1038\u1019\u103b\u102d\u102f\u1038\u101b\u103e\u102d\u101e\u100a\u103a\u1000\u102d\u102f \u101e\u1010\u102d\u1015\u103c\u102f\u101e\u1004\u1037\u103a\u101e\u100a\u103a\u104b \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1021\u101a\u1030\u1021\u1006\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101f\u102f\u101c\u100a\u103a\u1038 \u1001\u1031\u102b\u103a\u101e\u100a\u103a\u104b <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-prueba-de-hipotesis-para-la-media\"><\/span> \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u1021\u101a\u1030\u1021\u1006\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1010\u103d\u1000\u103a\u1006\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u1000\u1032\u1037\u101e\u102d\u102f\u1037 \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1000\u103c\u100a\u1037\u103a\u1015\u102b\u1019\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u101e\u100a\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u101e\u102d\u101e\u100a\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1019\u101e\u102d\u1015\u1031\u102b\u103a \u1019\u1030\u1010\u100a\u103a\u104d \u1021\u1014\u100a\u103a\u1038\u1004\u101a\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u101e\u100a\u103a\u104a \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u101e\u102d\u101e\u1031\u102c\u1021\u1001\u102b \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u101e\u102d\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u101e\u102d\u101e\u1031\u102c\u1021\u1001\u102b\u1010\u103d\u1004\u103a \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u1026\u1038\u1005\u103d\u102c\u1000\u103c\u100a\u1037\u103a\u101b\u103e\u102f\u1015\u102b\u1019\u100a\u103a\u104b<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"con-varianza-conocida\"><\/span> \u101e\u103d\u1031\u1016\u100a\u103a\u1001\u103c\u1004\u103a\u1038 \u1016\u103c\u1004\u1037\u103a \u101e\u102d\u101e\u100a\u103a\u104b<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u101e\u102d\u101b\u103e\u102d\u1011\u102c\u1038\u101e\u100a\u1037\u103a\u1021\u1010\u103d\u1000\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1021\u101a\u1030\u1021\u1006\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c<\/strong> \u1019\u103e\u102c-<\/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\"> \u101b\u103d\u103e\u1031-<\/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> \u1006\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1010\u103d\u1000\u103a hypothesis test statistic \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/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> \u1014\u1019\u1030\u1014\u102c\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u104b<\/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> \u1021\u1006\u102d\u102f\u1015\u103c\u102f\u1011\u102c\u1038\u101e\u1031\u102c \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/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> \u101c\u1030\u1026\u1038\u101b\u1031\u1005\u1036\u1014\u103e\u102f\u1014\u103a\u1038\u101e\u103d\u1031\u1016\u100a\u103a\u101e\u100a\u103a\u104b<\/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> \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/li>\n<\/ul>\n<p> \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1010\u103d\u1000\u103a\u1006\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1015\u103c\u102e\u1038\u101e\u100a\u103a\u1014\u103e\u1004\u1037\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a \u101b\u101c\u1012\u103a\u1000\u102d\u102f \u1021\u1013\u102d\u1015\u1039\u1015\u102c\u101a\u103a\u1015\u103c\u1014\u103a\u1006\u102d\u102f\u101e\u1004\u1037\u103a\u101e\u100a\u103a-<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1010\u103d\u1000\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u101e\u100a\u103a \u1014\u103e\u1005\u103a\u1016\u1000\u103a\u101e\u1018\u1031\u102c\u1010\u1030\u1015\u102b\u1000\u104a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u104f \u1015\u1000\u1010\u102d\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 Z <sub>\u03b1\/2<\/sub> \u1011\u1000\u103a \u1000\u103c\u102e\u1038\u1014\u1031\u1015\u102b\u1000 null hypothesis \u1000\u102d\u102f \u1015\u101a\u103a\u1001\u103b\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1010\u103d\u1000\u103a\u1006\u1001\u103b\u1000\u103a\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u101e\u100a\u103a \u1019\u103e\u1014\u103a\u1000\u1014\u103a\u101e\u1031\u102c\u1021\u1019\u103c\u102e\u1038\u1014\u103e\u1004\u1037\u103a\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u1000\u104a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u101e\u100a\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 Z <sub>\u03b1<\/sub> \u1011\u1000\u103a\u1000\u103c\u102e\u1038\u1015\u102b\u1000 null hypothesis \u1000\u102d\u102f \u1015\u101a\u103a\u1001\u103b\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1010\u103d\u1000\u103a\u1006\u1001\u103b\u1000\u103a\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u101e\u100a\u103a \u1018\u101a\u103a\u1021\u1019\u103c\u102e\u1038\u1014\u103e\u1004\u1037\u103a\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u1000\u104a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u101e\u100a\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 -Z <sub>\u03b1<\/sub> \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u1015\u102b\u1000 null hypothesis \u1000\u102d\u102f \u1015\u101a\u103a\u1001\u103b\u1015\u102b\u101e\u100a\u103a\u104b<\/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> \u1024\u1000\u102d\u1005\u1039\u1005\u1010\u103d\u1004\u103a\u104a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f <a href=\"https:\/\/statorials.org\/my\/\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u101b\u1031\u1038\u1007\u101a\u102c\u1038\/\">\u1005\u1036\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1001\u103b\u102e\u101b\u1031\u1038\u1007\u101a\u102c\u1038<\/a> \u1019\u103e \u101b\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"con-varianza-desconocida\"><\/span> \u1019\u101e\u102d\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1016\u103c\u1004\u1037\u103a<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>\u1021\u1019\u100a\u103a\u1019\u101e\u102d\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u1031\u102c \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1010\u103d\u1000\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c<\/strong> \u1019\u103e\u102c-<\/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-f8277d83b2d28325f25f5d118486200f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{s}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"75\" style=\"vertical-align: -34px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> \u101b\u103d\u103e\u1031-<\/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-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> <a href=\"https:\/\/statorials.org\/my\/\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1016\u103c\u1014\u1037\u103a\u101d\u1031\/\">\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f t \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f<\/a> \u1016\u103c\u1004\u1037\u103a \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1010\u103d\u1000\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/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> \u1014\u1019\u1030\u1014\u102c\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u104b<\/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> \u1021\u1006\u102d\u102f\u1015\u103c\u102f\u1011\u102c\u1038\u101e\u1031\u102c \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/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-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u1014\u1019\u1030\u1014\u102c\u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u101e\u100a\u103a\u104b<\/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> \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/li>\n<\/ul>\n<p> \u101a\u1001\u1004\u103a\u1000\u1032\u1037\u101e\u102d\u102f\u1037\u1015\u1004\u103a\u104a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u104f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1011\u102c\u1038\u101e\u1031\u102c\u101b\u101c\u1012\u103a\u101e\u100a\u103a null \u1021\u101a\u1030\u1021\u1006\u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1016\u103c\u1004\u1037\u103a \u1021\u1013\u102d\u1015\u1039\u1015\u102c\u101a\u103a\u1015\u103c\u1014\u103a\u1006\u102d\u102f\u101b\u1015\u102b\u1019\u100a\u103a-<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1010\u103d\u1000\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u101e\u100a\u103a \u1014\u103e\u1005\u103a\u1016\u1000\u103a\u101e\u1018\u1031\u102c\u1010\u1030\u1015\u102b\u1000\u104a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u104f \u1015\u1000\u1010\u102d\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 t <sub>\u03b1\/2|n-1<\/sub> \u1011\u1000\u103a\u1000\u103c\u102e\u1038\u1015\u102b\u1000 null hypothesis \u1000\u102d\u102f \u1015\u101a\u103a\u1001\u103b\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1010\u103d\u1000\u103a\u1006\u1001\u103b\u1000\u103a\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u101e\u100a\u103a \u1019\u103e\u1014\u103a\u1000\u1014\u103a\u101e\u1031\u102c\u1021\u1019\u103c\u102e\u1038\u1014\u103e\u1004\u1037\u103a\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u1000\u104a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u101e\u100a\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 t <sub>\u03b1|n-1<\/sub> \u1011\u1000\u103a\u1000\u103c\u102e\u1038\u1015\u102b\u1000 null hypothesis \u1000\u102d\u102f \u1015\u101a\u103a\u1001\u103b\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1010\u103d\u1000\u103a\u1006\u1001\u103b\u1000\u103a\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u101e\u100a\u103a \u1018\u101a\u103a\u1021\u1019\u103c\u102e\u1038\u1014\u103e\u1004\u1037\u103a\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u1000\u104a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u101e\u100a\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 -t <sub>\u03b1|n-1<\/sub> \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u1015\u102b\u1000 null hypothesis \u1000\u102d\u102f \u1015\u101a\u103a\u1001\u103b\u1015\u102b\u101e\u100a\u103a\u104b<\/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-31fb206b75a47181c7c673f54ba28ee8_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 } |t|>t_{\\alpha\/2|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu> \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t>t_{\\alpha|n-1} \\text{ se rechaza } H_0\\\\[3ex]H_1: \\mu< \\mu_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } t<-t_{\\alpha|n-1} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"112\" width=\"457\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u101e\u102d\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1007\u101a\u102c\u1038\u1019\u103e \u101b\u101a\u1030\u101e\u100a\u103a\u104b <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-prueba-de-hipotesis-para-la-media\"><\/span> \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u1021\u1005\u1005\u103a\u1021\u1019\u103e\u1014\u103a\u1000\u1019\u1039\u1018\u102c\u1014\u1019\u1030\u1014\u102c\u104a<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u101c\u1030\u1026\u1038\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u1037\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u104f \u101e\u1018\u1031\u102c\u1010\u101b\u102c\u1038\u1000\u102d\u102f \u1021\u1015\u103c\u100a\u1037\u103a\u1021\u101d\u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a\u104a \u1024\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u104f \u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1018\u101d\u1025\u1015\u1019\u102c\u1000\u102d\u102f \u1021\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a \u1000\u103c\u100a\u1037\u103a\u101b\u103e\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/p>\n<ul>\n<li> \u104e\u1004\u103a\u1038\u101c\u1000\u103a\u1015\u103a\u1010\u1031\u102c\u1037\u104f\u1018\u1000\u103a\u1011\u101b\u102e\u101e\u100a\u103a 6 \u1014\u102c\u101b\u102e\u1000\u103c\u102c\u1001\u1036\u101e\u100a\u103a\u101f\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1000\u102f\u1019\u1039\u1015\u100f\u102e\u1010\u1005\u103a\u1001\u102f\u1000\u1015\u103c\u1031\u102c\u1000\u103c\u102c\u1038\u1001\u1032\u1037\u101e\u100a\u103a\u104b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a \u03b1 = 0.05 \u1016\u103c\u1004\u1037\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1004\u1037\u103a \u1024\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u101e\u100a\u103a \u1019\u103e\u102c\u1038\u101a\u103d\u1004\u103a\u1038\u1001\u103c\u1004\u103a\u1038\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1005\u1005\u103a\u1006\u1031\u1038\u1015\u102b\u101e\u100a\u103a\u104b \u1012\u102e\u101c\u102d\u102f\u101c\u102f\u1015\u103a\u1016\u102d\u102f\u1037\u104a \u1021\u101c\u102f\u1036\u1038\u101b\u1031 20 \u1000\u102d\u102f\u101d\u101a\u103a\u1015\u103c\u102e\u1038 \u1000\u103d\u1014\u103a\u1015\u103b\u1030\u1010\u102c\u1010\u1005\u103a\u101c\u102f\u1036\u1038\u1005\u102e\u101b\u1032\u1037 \u1018\u1000\u103a\u1011\u101b\u102e\u101e\u1000\u103a\u1010\u1019\u103a\u1038\u1000\u102d\u102f \u1005\u1031\u102c\u1004\u1037\u103a\u1000\u103c\u100a\u1037\u103a\u1016\u102d\u102f\u1037 \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101c\u102d\u102f\u1000\u103a\u1010\u101a\u103a (\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1010\u103d\u1031\u1000\u102d\u102f \u1014\u102c\u101b\u102e\u1014\u1032\u1037 \u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1010\u101a\u103a)\u104b<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"> \u1045.\u1042 \u1045.\u1049 \u1047.\u1041 \u1044.\u1042 \u1046.\u1045<br \/> \u1048.\u1045 \u1044.\u1046 \u1046.\u1048 \u1046.\u1049 \u1045.\u1048<br \/> \u1045.\u1041 \u1046.\u1045 \u1047.\u1040 \u1045.\u1043 \u1046.\u1042<br \/> \u1045.\u1047 \u1046.\u1046 \u1047.\u1045 \u1045.\u1041 \u1046.\u1041<\/p>\n<p> \u1024\u1000\u102d\u1005\u1039\u1005\u1010\u103d\u1004\u103a\u104a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1014\u103e\u1004\u1037\u103a\u1015\u1010\u103a\u101e\u1000\u103a\u101e\u1031\u102c \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f <a href=\"https:\/\/statorials.org\/my\/null-\u1014\u103e\u1004\u1037\u103a-\u1021\u1005\u102c\u1038\u1011\u102d\u102f\u1038\u101a\u1030\u1006\u1001\u103b\u1000\u103a\/\">null \u1014\u103e\u1004\u1037\u103a \u1021\u1001\u103c\u102c\u1038\u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c \u1021\u101a\u1030\u1021\u1006\u1019\u103b\u102c\u1038\u101e\u100a\u103a<\/a> \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a-<\/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-329ffe392783b8bee1eef642d1a45f53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu=6\\\\[2ex] H_1:\\mu\\neq 6 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"93\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1005\u1036\u1014\u103e\u102f\u1014\u103a\u1038\u1014\u103e\u1004\u1037\u103a \u1014\u1019\u1030\u1014\u102c\u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1026\u1038\u1005\u103d\u102c\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a-<\/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-ef07dbee8f95fc767bc069bd738bb493_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\overline{x}=6,13 \\qquad s=1,05\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"169\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u101c\u1030\u1026\u1038\u101b\u1031\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1019\u101e\u102d\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1000\u102d\u102f\u101b\u101b\u103e\u102d\u101b\u1014\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1019\u100a\u103a\u1019\u101e\u102d\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u1031\u102c \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1010\u103d\u1000\u103a \u1010\u103d\u1031\u1038\u1001\u1031\u102b\u103a\u1019\u103e\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1014\u103a\u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a- <\/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-f8277d83b2d28325f25f5d118486200f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\overline{x}-\\mu}{\\displaystyle \\frac{s}{\\sqrt{n}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"57\" width=\"75\" style=\"vertical-align: -34px;\"><\/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-447879c9f526afed74796d347fd69c97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{6,13-6}{\\displaystyle \\frac{1,05}{\\sqrt{20}}} \" title=\"Rendered by QuickLaTeX.com\" height=\"62\" width=\"98\" style=\"vertical-align: -38px;\"><\/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-e0e63621349c12eec107c43152b5213c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=0,68\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u101a\u1001\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f \u1021\u101b\u1031\u1038\u1015\u102b\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a\u104a \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1021\u1010\u103d\u1000\u103a <a href=\"https:\/\/statorials.org\/my\/\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038-t-\u1016\u103c\u1014\u1037\u103a\u1001\u103b\u102e\u101b\u1031\u1038\u1007\u101a\u102c\u1038\/\">\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f t \u1016\u103c\u1014\u1037\u103a\u1001\u103b\u102e\u101b\u1031\u1038\u1007\u101a\u102c\u1038<\/a> \u1010\u103d\u1004\u103a \u1000\u103c\u100a\u1037\u103a\u101b\u103e\u102f\u1015\u102b\u104b Student&#8217;s t \u104f \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038 (20-1=19) \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u1015\u103c\u102e\u1038 \u1021\u1001\u103c\u102c\u1038\u1010\u1005\u103a\u1016\u1000\u103a\u1010\u103d\u1004\u103a\u104a \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101b\u102c\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u100a\u103a \u1014\u103e\u1005\u103a\u1018\u1000\u103a\u101c\u102f\u1036\u1038\u1016\u103c\u1005\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1011\u1000\u103a\u101d\u1000\u103a (0.05\/2= 0.025) \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b hypothesis \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u104b<\/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-8154fa6e5bfee35698c6dc26928cd98c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha=0,05 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black}\\ \\alpha\/2=0,025\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"300\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e85692dfb2fb2522025566dc205b8117_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}t_{\\alpha\/2| n-1}= \\ \\color{orange}\\bm{?}\\\\[4ex]t_{0,025| 19}=2,093\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"72\" width=\"152\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u1014\u102d\u1002\u102f\u1036\u1038\u1001\u103b\u102f\u1015\u103a\u1021\u1014\u1031\u1016\u103c\u1004\u1037\u103a\u104a \u1024\u101e\u100a\u103a\u1019\u103e\u102c \u1014\u103e\u1005\u103a\u1016\u1000\u103a\u1019\u103c\u1004\u103a\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u104f \u1015\u1000\u1010\u102d\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a null hypothesis \u1000\u102d\u102f \u1015\u101a\u103a\u1001\u103b\u1019\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u1021\u1001\u103c\u102c\u1038\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1021\u102c\u1038 \u1015\u101a\u103a\u1001\u103b\u1015\u102b\u101e\u100a\u103a\u104b <\/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-0e46ceecc8ebcda6dd88ec4d3771c285_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"0,68<2,093 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Se rechaza } H_1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"345\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-de-hipotesis-para-la-diferencia-de-medias\"><\/span> \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1019\u103e\u102c \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u101a\u1030\u1006\u1001\u103b\u1000\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u104b<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>\u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1001\u103b\u1000\u103a \u1006\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u101c\u1030\u1014\u103e\u1005\u103a\u1026\u1038\u104f \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1019\u103e\u102c \u1010\u1030\u100a\u102e\u101e\u100a\u103a\u101f\u1030\u101e\u1031\u102c null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u101c\u1000\u103a\u1001\u1036\u101b\u1014\u103a \u1021\u101a\u1030\u1021\u1006 \u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f<\/strong> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/p>\n<p> \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1014\u103e\u1005\u103a\u1019\u103b\u102d\u102f\u1038\u104f \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u104f null hypothesis \u101e\u100a\u103a \u1021\u1019\u103c\u1032\u1010\u1019\u103a\u1038 \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a \u104b<\/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-2945a64bf97e1c02ac7fb56bbf1f215b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"H_0: \\mu_1=\\mu_2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"97\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> \u1021\u1005\u102c\u1038\u1011\u102d\u102f\u1038\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u101e\u102f\u1036\u1038\u1019\u103b\u102d\u102f\u1038\u1011\u1032\u1019\u103e \u1010\u1005\u103a\u1001\u102f \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038\u104a<\/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-c612ac7651faad9faa195f37fdf6edef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1:\\mu_1\\neq \\mu_2\\\\[2ex]H_1:\\mu_1>\\mu_2\\\\[2ex]H_1:\\mu_1<\\mu_2\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"92\" width=\"97\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a <strong>\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u101e\u102d\u101b\u103e\u102d\u101e\u100a\u1037\u103a\u1021\u1001\u102b \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u101a\u1030\u1021\u1006\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1019\u103e\u102c<\/strong> &#8211;<\/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-83c9d3ddf8c2ff8b9cf2b0fa4ac8082e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\displaystyle \\overline{x_1}-\\overline{x_2}}{\\displaystyle\\sqrt{\\frac{\\sigma_1^2}{n_1}+\\frac{\\sigma_2^2}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"75\" width=\"123\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> \u101b\u103d\u103e\u1031-<\/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> \u1005\u1036\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1014\u1031\u102c\u1000\u103a\u1006\u1000\u103a\u1010\u103d\u1032\u1016\u103c\u1005\u103a\u101e\u1031\u102c \u101e\u102d\u1011\u102c\u1038\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1016\u103c\u1004\u1037\u103a \u1006\u102d\u102f\u101c\u102d\u102f\u1001\u103b\u1000\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u104f \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1016\u103c\u1005\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/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> \u1014\u1019\u1030\u1014\u102c 1 \u104f \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/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> \u1014\u1019\u1030\u1014\u102c 2 \u104f \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/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-c2e8ce841b1fc1e199b133e6f24f6f51_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_1^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"18\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u101c\u1030\u1026\u1038\u101b\u1031 \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f \u1041\u104b<\/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-d5fd430c9ff19057933c215e683ace41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sigma_2^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"18\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u101c\u1030\u1026\u1038\u101b\u1031 \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f \u1042\u104b<\/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> \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038 1 \u1016\u103c\u1005\u103a\u1015\u102b\u1010\u101a\u103a\u104b<\/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> \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038 2 \u1016\u103c\u1005\u103a\u1015\u102b\u1010\u101a\u103a\u104b<\/li>\n<\/ul>\n<p> \u1021\u1001\u103c\u102c\u1038\u1010\u1005\u103a\u1016\u1000\u103a\u1010\u103d\u1004\u103a\u104a <strong>\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u101e\u102d\u101b\u103e\u102d\u101e\u100a\u1037\u103a\u1021\u1001\u102b \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u101a\u1030\u1006\u1001\u103b\u1000\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1019\u103e\u102c<\/strong> \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/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-e9fbc7bf6d5bbaeb18a3992a3f373a55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle \\overline{x_1}-\\overline{x_2}}{\\displaystyle\\sqrt{\\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"75\" width=\"317\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> \u101b\u103d\u103e\u1031-<\/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-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f t \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102d\u102f\u1000\u103a\u1014\u102c\u101e\u1031\u102c \u1021\u1019\u100a\u103a\u1019\u101e\u102d\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1016\u103c\u1004\u1037\u103a \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u1037\u103a \u1014\u103e\u1005\u103a\u1001\u102f\u104f \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u102c\u1014\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/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> \u1014\u1019\u1030\u1014\u102c 1 \u104f \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/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> \u1014\u1019\u1030\u1014\u102c 2 \u104f \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/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-59ae3c411ec80f65d56e397f87d29753_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_1^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"15\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u1014\u1019\u1030\u1014\u102c 1 \u104f\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/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-c785df8c080b6984c6205f881426fb10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_2^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"15\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u1014\u1019\u1030\u1014\u102c 2 \u104f\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/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> \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038 1 \u1016\u103c\u1005\u103a\u1015\u102b\u1010\u101a\u103a\u104b<\/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> \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038 2 \u1016\u103c\u1005\u103a\u1015\u102b\u1010\u101a\u103a\u104b<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u1024\u1006\u1031\u102c\u1004\u103a\u1038\u1015\u102b\u1038\u101e\u100a\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1006\u102d\u102f\u101c\u102d\u102f\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u1019\u100a\u103a\u1000\u1032\u1037\u101e\u102d\u102f\u1037\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u1021\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u101e\u1004\u103a\u101e\u100a\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1010\u103d\u1000\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1000\u102d\u102f \u1010\u103d\u1031\u1037\u101b\u1019\u100a\u103a\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038\u104a \u1011\u102d\u102f\u1037\u1021\u1015\u103c\u1004\u103a \u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u1001\u1014\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1015\u103c\u102e\u1038\u1010\u1005\u103a\u1001\u102f \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a\u1016\u103c\u1031\u101b\u103e\u1004\u103a\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a hypothesis testing \u1006\u102d\u102f\u1010\u102c \u1018\u102c\u101c\u1032\u104b \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1010\u103d\u1000\u103a \u1010\u103d\u1031\u1038\u1001\u1031\u102b\u103a\u1019\u103e\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038 \u101e\u100a\u103a \u101c\u1030\u1026\u1038\u101b\u1031\u1006\u102d\u102f\u101c\u102d\u102f\u1001\u103b\u1000\u103a\u104f null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1015\u102d\u102f\u104d\u1010\u102d\u1000\u103b\u101e\u100a\u103a\u1019\u103e\u102c\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u1010\u103d\u1004\u103a \u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103c\u1004\u103a\u1038\u1014\u103e\u1004\u1037\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1001\u103c\u1004\u103a\u1038 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1019\u1004\u103c\u1004\u103a\u1038\u101b\u1014\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1014\u103e\u1004\u1037\u103a \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1001\u103c\u1004\u103a\u1038\u1010\u102d\u102f\u1037 \u1015\u102b\u101d\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u1019\u100a\u103a\u1021\u1019\u103b\u102d\u102f\u1038\u1019\u103b\u102d\u102f\u1038\u101b\u103e\u102d\u101e\u100a\u103a\u1000\u102d\u102f \u101e\u1010\u102d\u1015\u103c\u102f\u101e\u1004\u1037\u103a\u101e\u100a\u103a\u104b \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1021\u101a\u1030\u1021\u1006\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101f\u102f\u101c\u100a\u103a\u1038 \u1001\u1031\u102b\u103a\u101e\u100a\u103a\u104b [&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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a Hypothesis 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