{"id":285,"date":"2023-08-03T03:11:14","date_gmt":"2023-08-03T03:11:14","guid":{"rendered":"https:\/\/statorials.org\/tr\/ortalamalar-arasindaki-farka-yonelik-hipotez-testi\/"},"modified":"2023-08-03T03:11:14","modified_gmt":"2023-08-03T03:11:14","slug":"ortalamalar-arasindaki-farka-yonelik-hipotez-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ortalamalar-arasindaki-farka-yonelik-hipotez-testi\/","title":{"rendered":"Ortalamalardaki fark i\u00e7in hipotez testi"},"content":{"rendered":"<p>Bu makale istatistikte ortalama hipotez testinin ne gibi bir fark yaratt\u0131\u011f\u0131n\u0131 ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131 a\u00e7\u0131klamaktad\u0131r. Benzer \u015fekilde, ortalamalar aras\u0131ndaki farka ili\u015fkin bir hipotez testinin nas\u0131l yap\u0131laca\u011f\u0131n\u0131 ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ke\u015ffedeceksiniz. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-prueba-de-hipotesis-para-la-diferencia-de-medias\"><\/span> Ortalama fark i\u00e7in hipotez testi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Ortalamalardaki fark i\u00e7in hipotez testi,<\/strong> iki pop\u00fclasyonun ortalamalar\u0131n\u0131n farkl\u0131 oldu\u011fu hipotezini reddetmek veya kabul etmek i\u00e7in kullan\u0131lan istatistiksel bir testtir. Yani, ortalamalar aras\u0131ndaki fark hipotez testi, iki pop\u00fclasyonun ortalamalar\u0131n\u0131n ayn\u0131 m\u0131 yoksa farkl\u0131 m\u0131 oldu\u011funu belirlemek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Hipotez testinde al\u0131nan kararlar\u0131n \u00f6nceden belirlenmi\u015f bir <a href=\"https:\/\/statorials.org\/tr\/bir-guven-seviyesi\/\">g\u00fcven d\u00fczeyine<\/a> dayand\u0131\u011f\u0131n\u0131, dolay\u0131s\u0131yla bir hipotez testinin sonucunun her zaman do\u011fru oldu\u011funu garanti edemeyece\u011fini, bunun yerine en olas\u0131 sonucun do\u011fru oldu\u011funu unutmay\u0131n.<\/p>\n<p> \u0130ki ortalaman\u0131n fark\u0131na y\u00f6nelik hipotez testi, test istatisti\u011finin hesaplanmas\u0131n\u0131 ve bo\u015f hipotezin reddedilip reddedilmeyece\u011fini kritik de\u011ferle kar\u015f\u0131la\u015ft\u0131rmay\u0131 i\u00e7erir. A\u015fa\u011f\u0131da ortalamalar aras\u0131ndaki fark i\u00e7in bir hipotez testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fini g\u00f6rece\u011fiz.<\/p>\n<p> Son olarak, istatistikte hipotez testine hipotez kar\u015f\u0131tl\u0131klar\u0131, hipotez testi veya anlaml\u0131l\u0131k testi de denilebilece\u011fini unutmay\u0131n. <\/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>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/ortalamalar-farkinin-ornekleme-dagilimi\/\">Ortalamalardaki fark\u0131n \u00f6rnekleme da\u011f\u0131l\u0131m\u0131<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-prueba-de-hipotesis-para-la-diferencia-de-medias\"><\/span> Ortalamalardaki Fark i\u00e7in Hipotez Testi Form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ortalamalardaki farka ili\u015fkin hipotezleri test etmek i\u00e7in kullan\u0131lmas\u0131 gereken form\u00fcl, pop\u00fclasyon varyanslar\u0131n\u0131n bilinip bilinmedi\u011fine ve bilinmiyorsa bunlar\u0131n ayn\u0131 veya farkl\u0131 oldu\u011funun varsay\u0131l\u0131p varsay\u0131lamayaca\u011f\u0131na ba\u011fl\u0131 olarak de\u011fi\u015fir. Yani bu b\u00f6l\u00fcmde duruma g\u00f6re hangi form\u00fcl\u00fcn kullan\u0131laca\u011f\u0131n\u0131 g\u00f6rece\u011fiz.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-conocidas\"><\/span> Bilinen varyasyonlar<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Varyanslar bilindi\u011finde ortalamalar aras\u0131ndaki farka ili\u015fkin hipotez testi istatisti\u011fini hesaplama form\u00fcl\u00fc<\/strong> a\u015fa\u011f\u0131daki gibidir:<\/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\"> Alt\u0131n:<\/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> standart normal da\u011f\u0131l\u0131ma uyan, bilinen varyansa sahip iki ortalaman\u0131n fark\u0131 i\u00e7in hipotez test istatisti\u011fidir.<\/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> n\u00fcfus 1&#8217;in ortalamas\u0131d\u0131r.<\/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> n\u00fcfus 2&#8217;nin ortalamas\u0131d\u0131r.<\/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> \u00f6rnek 1&#8217;in ortalamas\u0131d\u0131r.<\/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> \u00f6rnek 2&#8217;nin ortalamas\u0131d\u0131r.<\/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> pop\u00fclasyon 1&#8217;in standart sapmas\u0131d\u0131r.<\/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> pop\u00fclasyon 2&#8217;nin standart sapmas\u0131d\u0131r.<\/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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 1&#8217;dir.<\/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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 2&#8217;dir.<\/li>\n<\/ul>\n<p> Bunun en az g\u00f6r\u00fclen durum oldu\u011funu unutmay\u0131n, dolay\u0131s\u0131yla bu form\u00fcl yaln\u0131zca baz\u0131 \u00f6zel durumlarda kullan\u0131l\u0131r.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-desconocidas-e-iguales\"><\/span> Bilinmeyen ve e\u015fit sapmalar<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Pop\u00fclasyon varyanslar\u0131n\u0131n bilinmedi\u011fi ancak e\u015fit oldu\u011fu varsay\u0131ld\u0131\u011f\u0131nda ortalamalar aras\u0131ndaki farka ili\u015fkin hipotez testi istatisti\u011fini hesaplama form\u00fcl\u00fc \u015f\u00f6yledir<\/strong> :<\/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-b879974c3d05ebcb049125dbaf9f0a48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle (\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle s_p\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"67\" width=\"197\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/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> <sub>n1<\/sub> + <sub>n2-2<\/sub> serbestlik derecesine sahip bir \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131 takip eden, bilinmeyen varyanslara sahip ortalamalar aras\u0131ndaki farka y\u00f6nelik hipotez test istatisti\u011fidir.<\/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> n\u00fcfus 1&#8217;in ortalamas\u0131d\u0131r.<\/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> n\u00fcfus 2&#8217;nin ortalamas\u0131d\u0131r.<\/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> \u00f6rnek 1&#8217;in ortalamas\u0131d\u0131r.<\/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> \u00f6rnek 2&#8217;nin ortalamas\u0131d\u0131r.<\/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-db24109a40d5779feee64c7bccc11371_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s_p\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"15\" style=\"vertical-align: -6px;\"><\/p>\n<p> birle\u015fik standart sapmad\u0131r.<\/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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 1&#8217;dir.<\/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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 2&#8217;dir.<\/li>\n<\/ul>\n<p> \u0130ki numunenin birle\u015fik standart sapmas\u0131 a\u015fa\u011f\u0131daki form\u00fclle hesaplan\u0131r: <\/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-a8fb43d179e453d19f5781319aa9e1ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle s_p=\\sqrt{\\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"240\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"varianzas-desconocidas-y-diferentes\"><\/span> Bilinmeyen ve farkl\u0131 varyasyonlar<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Pop\u00fclasyon varyanslar\u0131 bilinmedi\u011finde ve ayr\u0131ca farkl\u0131 olduklar\u0131 varsay\u0131ld\u0131\u011f\u0131nda, ortalamalar aras\u0131ndaki farka ili\u015fkin hipotez testi istatisti\u011fini hesaplama form\u00fcl\u00fc a\u015fa\u011f\u0131daki gibidir:<\/strong><\/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-01c79415ff9c173fa4517d4b1a859a8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle (\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle \\sqrt{\\frac{s_1^2}{n_1}+\\frac{s_2^2}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"197\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Alt\u0131n:<\/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> \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131 takip eden, bilinmeyen varyanslara sahip ortalamalar aras\u0131ndaki farka y\u00f6nelik hipotez test istatisti\u011fidir.<\/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> n\u00fcfus 1&#8217;in ortalamas\u0131d\u0131r.<\/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> n\u00fcfus 2&#8217;nin ortalamas\u0131d\u0131r.<\/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> \u00f6rnek 1&#8217;in ortalamas\u0131d\u0131r.<\/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> \u00f6rnek 2&#8217;nin ortalamas\u0131d\u0131r.<\/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> pop\u00fclasyon 1&#8217;in standart sapmas\u0131d\u0131r.<\/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> pop\u00fclasyon 2&#8217;nin standart sapmas\u0131d\u0131r.<\/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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 1&#8217;dir.<\/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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 2&#8217;dir.<\/li>\n<\/ul>\n<p> Ancak bu durumda \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131n serbestlik dereceleri a\u015fa\u011f\u0131daki form\u00fcl kullan\u0131larak hesaplan\u0131r: <\/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-ecf1ccfa1ecb47b889c569e5faa65a78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle GL=\\frac{\\displaystyle\\left(\\frac{s_1^2}{n_1}+\\frac{s_2^2}{n_2}\\right)^2}{\\displaystyle\\frac{\\displaystyle\\frac{s_1^2}{n_1}}{n_1-1}+\\frac{\\displaystyle\\frac{s_2^2}{n_2}}{n_2-1}}\" title=\"Rendered by QuickLaTeX.com\" height=\"115\" width=\"180\" style=\"vertical-align: -61px;\"><\/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>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/ortalamalardaki-fark-icin-guven-araligi\/\">Ortalamalar\u0131n fark\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131 form\u00fcl\u00fc<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-prueba-de-hipotesis-para-la-diferencia-de-medias\"><\/span> Ortalamalardaki fark i\u00e7in hipotez testinin somut \u00f6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ortalamalar aras\u0131ndaki farka ili\u015fkin hipotez testi kavram\u0131n\u0131 \u00f6z\u00fcmsemeyi bitirmek i\u00e7in, bu t\u00fcr hipotez testinin somut bir \u00f6rne\u011fini g\u00f6rece\u011fiz.<\/p>\n<ul>\n<li> Rakip iki \u015firketin maa\u015flar\u0131 \u00fczerine istatistiksel bir \u00e7al\u0131\u015fma yapmak istiyorsunuz, daha spesifik olarak iki \u015firketin ortalama maa\u015flar\u0131n\u0131n farkl\u0131 olup olmad\u0131\u011f\u0131n\u0131 belirlemek istiyorsunuz. Bunun i\u00e7in bir firmadan 47 i\u015f\u00e7iden, di\u011fer firmadan ise 55 i\u015f\u00e7iden numune al\u0131n\u0131r. Birinci \u00f6rnekten ortalama 40.000 ABD Dolar\u0131 maa\u015f ve 12.000 ABD Dolar\u0131 standart sapma elde edilirken, ikinci \u00f6rnekten ortalama 46.000 ABD Dolar\u0131 maa\u015f ve 18.000 ABD Dolar\u0131 standart sapma elde edilmi\u015ftir. Ortalama maa\u015flar\u0131n farkl\u0131 olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in %5 anlaml\u0131l\u0131k d\u00fczeyinde bir hipotez testi yap\u0131n.<\/li>\n<\/ul>\n<p> Bu durumda iki ortalaman\u0131n fark\u0131na ili\u015fkin hipotez testinin <a href=\"https:\/\/statorials.org\/tr\/bos-ve-alternatif-hipotez\/\">s\u0131f\u0131r hipotezi ve alternatif hipotezi<\/a> a\u015fa\u011f\u0131daki gibidir:<\/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-4dd9e80c0a87987d689d7b8d99be9d90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{cases}H_0: \\mu_1-\\mu_2=0\\\\[2ex] H_1:\\mu_1-\\mu_2\\neq 0 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"141\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Bu durumda n\u00fcfus farklar\u0131 bilinmemekle birlikte rakip \u015firketler olmalar\u0131 ve faaliyet g\u00f6sterdikleri pazar\u0131n \u00e7al\u0131\u015fma ko\u015fullar\u0131n\u0131n birbirine \u00e7ok benzer olmas\u0131 nedeniyle e\u015fit oldu\u011fu varsay\u0131labilir. Bu nedenle, ortalamalar aras\u0131ndaki farka ili\u015fkin hipotez test istatisti\u011fi i\u00e7in kullanmam\u0131z gereken form\u00fcl \u015f\u00f6yledir:<\/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-b879974c3d05ebcb049125dbaf9f0a48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle (\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle s_p\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"67\" width=\"197\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p> Bu nedenle iki numunenin birle\u015ftirilmi\u015f standart sapmas\u0131n\u0131 hesapl\u0131yoruz:<\/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-0308363d68c4677761d44b214b1609d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}\\displaystyle s_p&amp;=\\sqrt{\\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}\\\\[2ex]\\displaystyle s_p&amp;=\\sqrt{\\frac{(47-1)\\cdot 12000^2+(55-1)\\cdot 18000^2}{47+55-2}}\\\\[2ex]s_p&amp;=15530,61\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"161\" width=\"337\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> \u015eimdi ortalamalar aras\u0131ndaki fark i\u00e7in hipotez testi form\u00fcl\u00fcn\u00fc uyguluyoruz:<\/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-c5bf7791d156d1d7593182a7ffc64417_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle t=\\frac{\\displaystyle (\\overline{x_1}-\\overline{x_2})-(\\mu_1-\\mu_2)}{\\displaystyle s_p\\sqrt{\\frac{1}{n_1}+\\frac{1}{n_2}}}=\\cfrac{(40000-46000)-0}{\\displaystyle 15530,61\\sqrt{\\frac{1}{47}+\\frac{1}{55}}}=-1,94\" title=\"Rendered by QuickLaTeX.com\" height=\"69\" width=\"451\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p> \u00d6te yandan, ortalamalar aras\u0131ndaki fark i\u00e7in hipotez testinin kritik de\u011ferini <a href=\"https:\/\/statorials.org\/tr\/ogrenci-t-dagilim-tablosu\/\">\u00d6\u011frenci t tablosunda<\/a> arar\u0131z:<\/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-d5f11ecd0336e50c63b0ab2fab4bd530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}t_{\\alpha\/2| n_1+n_2-2}= \\ \\color{orange}\\bm{?}\\\\[4ex]t_{0,025| 100}=1,984\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"72\" width=\"184\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Daha sonra test istatisti\u011finin mutlak de\u011feri kritik test de\u011ferinden k\u00fc\u00e7\u00fck oldu\u011fundan s\u0131f\u0131r hipotezi kabul edilir ve alternatif hipotez reddedilir.<\/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-ca4a2499b93203ce31a36a1cbacbcc8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"|-1,94|=1,94<1,984 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Se rechaza } H_1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"432\" style=\"vertical-align: -5px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bu makale istatistikte ortalama hipotez testinin ne gibi bir fark yaratt\u0131\u011f\u0131n\u0131 ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131n\u0131 a\u00e7\u0131klamaktad\u0131r. Benzer \u015fekilde, ortalamalar aras\u0131ndaki farka ili\u015fkin bir hipotez testinin nas\u0131l yap\u0131laca\u011f\u0131n\u0131 ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir al\u0131\u015ft\u0131rmay\u0131 ke\u015ffedeceksiniz. Ortalama fark i\u00e7in hipotez testi nedir? Ortalamalardaki fark i\u00e7in hipotez testi, iki pop\u00fclasyonun ortalamalar\u0131n\u0131n farkl\u0131 oldu\u011fu hipotezini reddetmek veya kabul etmek [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-285","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u25b7 Ortalamalar aras\u0131ndaki fark i\u00e7in hipotez testi<\/title>\n<meta name=\"description\" content=\"Burada ortalamalar aras\u0131ndaki farka y\u00f6nelik hipotez testinin ne oldu\u011funu, nas\u0131l ger\u00e7ekle\u015ftirildi\u011fini (form\u00fcl) ve ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclm\u00fc\u015f bir \u00f6rne\u011fi bulacaks\u0131n\u0131z.\" \/>\n<meta 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