{"id":261,"date":"2023-08-03T11:26:47","date_gmt":"2023-08-03T11:26:47","guid":{"rendered":"https:\/\/statorials.org\/tr\/ortalama-icin-hipotez-testi\/"},"modified":"2023-08-03T11:26:47","modified_gmt":"2023-08-03T11:26:47","slug":"ortalama-icin-hipotez-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ortalama-icin-hipotez-testi\/","title":{"rendered":"Ortalama i\u00e7in hipotez testi"},"content":{"rendered":"<p>Bu makale istatistikte ortalamaya ili\u015fkin hipotez testinin ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece ortalama i\u00e7in hipotez testi form\u00fcl\u00fcn\u00fc ve ayr\u0131ca ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclen bir al\u0131\u015ft\u0131rmay\u0131 bulacaks\u0131n\u0131z. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-prueba-de-hipotesis-para-la-media\"><\/span> Ortalama i\u00e7in hipotez testi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Ortalama i\u00e7in hipotez testi,<\/strong> bir pop\u00fclasyon ortalamas\u0131n\u0131n s\u0131f\u0131r hipotezini reddetmek veya reddetmek i\u00e7in kullan\u0131lan istatistiksel bir y\u00f6ntemdir.<\/p>\n<p> Daha spesifik olarak, ortalama i\u00e7in hipotez testi, test istatisti\u011finin hesaplanmas\u0131n\u0131 ve s\u0131f\u0131r hipotezinin reddedilip reddedilmeyece\u011fini kritik de\u011ferle kar\u015f\u0131la\u015ft\u0131rmay\u0131 i\u00e7erir.<\/p>\n<p> Hipotez testlerinin farkl\u0131 isimlere sahip oldu\u011funu belirtmek gerekir; istatistiklerde bunlara hipotez kar\u015f\u0131tl\u0131klar\u0131, hipotez testleri veya anlaml\u0131l\u0131k testleri de denir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-prueba-de-hipotesis-para-la-media\"><\/span> Ortalama i\u00e7in Hipotez Testi Form\u00fcl\u00fc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Daha sonra ortalama i\u00e7in hipotez testi istatisti\u011finin nas\u0131l hesapland\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz. Bununla birlikte, varyans\u0131n bilinip bilinmemesine ba\u011fl\u0131 olarak form\u00fcl biraz de\u011fi\u015fir, bu nedenle \u00f6nce varyans bilindi\u011finde ve sonra varyans bilinmedi\u011finde bunun nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 g\u00f6rece\u011fiz.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"con-varianza-conocida\"><\/span> Bilinen sapma ile<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Bilinen varyansl\u0131 ortalama i\u00e7in test hipotezi form\u00fcl\u00fc<\/strong> \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-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\"> 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> ortalama i\u00e7in hipotez testi 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-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> \u00f6rnek anlam\u0131na gelir.<\/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> \u00f6nerilen ortalama de\u011ferdir.<\/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> n\u00fcfus 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-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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/li>\n<\/ul>\n<p> Ortalama i\u00e7in hipotez testi istatisti\u011fi hesapland\u0131ktan sonra sonu\u00e7, s\u0131f\u0131r hipotezini reddedecek veya reddedecek \u015fekilde yorumlanmal\u0131d\u0131r:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Ortalama i\u00e7in hipotez testi iki tarafl\u0131 ise, istatisti\u011fin mutlak de\u011feri Z <sub>\u03b1\/2<\/sub> kritik de\u011ferinden b\u00fcy\u00fckse s\u0131f\u0131r hipotezi reddedilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Ortalamaya y\u00f6nelik hipotez testi sa\u011f kuyrukla e\u015fle\u015fiyorsa, istatisti\u011fin Z <sub>\u03b1<\/sub> kritik de\u011ferinden b\u00fcy\u00fck olmas\u0131 durumunda s\u0131f\u0131r hipotezi reddedilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Ortalama i\u00e7in hipotez testi sol kuyrukla e\u015fle\u015firse, istatistik kritik de\u011fer -Z <sub>\u03b1&#8217;dan<\/sub> k\u00fc\u00e7\u00fckse s\u0131f\u0131r hipotezi reddedilir.<\/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> Bu durumda kritik de\u011ferler <a href=\"https:\/\/statorials.org\/tr\/normal-dagilim-tablosu\/\">standartla\u015ft\u0131r\u0131lm\u0131\u015f normal da\u011f\u0131l\u0131m tablosundan<\/a> elde edilir.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"con-varianza-desconocida\"><\/span> Bilinmeyen varyansla<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Bilinmeyen varyansl\u0131 ortalama i\u00e7in test hipotezi form\u00fcl\u00fc<\/strong> \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-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\"> 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> Ortalamaya ili\u015fkin hipotez test istatisti\u011fidir ve bu, <a href=\"https:\/\/statorials.org\/tr\/ogrenci-dagilimi\/\">\u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131<\/a> ile tan\u0131mlan\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-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> \u00f6rnek anlam\u0131na gelir.<\/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> \u00f6nerilen ortalama de\u011ferdir.<\/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> \u00f6rnek 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-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> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcd\u00fcr.<\/li>\n<\/ul>\n<p> Daha \u00f6nce oldu\u011fu gibi, test istatisti\u011finin hesaplanan sonucu, bo\u015f hipotezin reddedilmesi veya reddedilmemesi i\u00e7in kritik de\u011ferle yorumlanmal\u0131d\u0131r:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Ortalamaya y\u00f6nelik hipotez testi iki tarafl\u0131 ise, istatisti\u011fin mutlak de\u011feri <sub>t\u03b1\/2|n-1<\/sub> kritik de\u011ferinden b\u00fcy\u00fckse s\u0131f\u0131r hipotezi reddedilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Ortalama i\u00e7in hipotez testi sa\u011f kuyrukla e\u015fle\u015fiyorsa, istatisti\u011fin <sub>t\u03b1|n-1<\/sub> kritik de\u011ferinden b\u00fcy\u00fck olmas\u0131 durumunda s\u0131f\u0131r hipotezi reddedilir.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Ortalama i\u00e7in hipotez testi sol kuyrukla e\u015fle\u015firse, istatistik kritik de\u011fer -t <sub>\u03b1|n-1&#8217;den<\/sub> k\u00fc\u00e7\u00fckse s\u0131f\u0131r hipotezi reddedilir.<\/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> Varyans\u0131n bilinmedi\u011fi durumlarda kritik test de\u011ferleri \u00d6\u011frenci da\u011f\u0131l\u0131m tablosundan elde edilir. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-resuelto-de-la-prueba-de-hipotesis-para-la-media\"><\/span> Ortalama i\u00e7in Ger\u00e7ek D\u00fcnyadan Hipotez Testi \u00d6rne\u011fi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> N\u00fcfus ortalamas\u0131na y\u00f6nelik hipotez testi kavram\u0131n\u0131 tam olarak anlamak i\u00e7in, a\u015fa\u011f\u0131da bu t\u00fcr hipotez testinin ger\u00e7ek hayattan bir \u00f6rne\u011fini g\u00f6rebilirsiniz.<\/p>\n<ul>\n<li> Bir teknoloji \u015firketi satt\u0131\u011f\u0131 diz\u00fcst\u00fc bilgisayar\u0131n pilinin 6 saat dayand\u0131\u011f\u0131n\u0131 iddia ediyor. Bu hipotezin yanl\u0131\u015f olup olmad\u0131\u011f\u0131n\u0131, anlaml\u0131l\u0131k seviyesi \u03b1 = 0,05 olan bir hipotez testi yaparak kontrol ediyoruz. Bunun i\u00e7in 20 adet sat\u0131n al\u0131nmas\u0131na ve her bilgisayar\u0131n pil \u00f6mr\u00fcn\u00fcn g\u00f6zlemlenmesine karar verilir (de\u011ferler saat cinsinden ifade edilmi\u015ftir):<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"> 5,2 5,9 7,1 4,2 6,5<br \/> 8,5 4,6 6,8 6,9 5,8<br \/> 5,1 6,5 7,0 5,3 6,2<br \/> 5,7 6,6 7,5 5,1 6,1<\/p>\n<p> Bu durumda hipotez testinin ortalamaya ili\u015fkin <a href=\"https:\/\/statorials.org\/tr\/bos-ve-alternatif-hipotez\/\">s\u0131f\u0131r ve alternatif hipotezleri<\/a> \u015fu \u015fekildedir:<\/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> Test istatisti\u011fini belirlemek i\u00e7in \u00f6ncelikle \u00f6rnek ortalamas\u0131n\u0131 ve \u00f6rnek standart sapmas\u0131n\u0131 hesaplamam\u0131z gerekir:<\/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> Pop\u00fclasyon varyans\u0131n\u0131 bilmedi\u011fimizden, test istatisti\u011fini elde etmek i\u00e7in bilinmeyen varyansl\u0131 ortalamaya y\u00f6nelik hipotez test form\u00fcl\u00fcn\u00fc uygulamam\u0131z gerekir: <\/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> \u015eimdi hipotez testinin kritik de\u011ferini bulmam\u0131z gerekiyor, dolay\u0131s\u0131yla kar\u015f\u0131l\u0131k gelen de\u011fer i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/ogrenci-t-dagilim-tablosu\/\">\u00d6\u011frenci t da\u011f\u0131l\u0131m tablosuna<\/a> bak\u0131yoruz. \u00d6\u011frenci t&#8217;sinin serbestlik derecesi \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcnden bir eksiktir (20-1=19) ve buna kar\u015f\u0131n kar\u015f\u0131l\u0131k gelen olas\u0131l\u0131k iki y\u00f6nl\u00fc oldu\u011fundan anlaml\u0131l\u0131k d\u00fczeyinin yar\u0131s\u0131 kadard\u0131r (0.05\/2= 0.025). hipotez testi.<\/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> Sonu\u00e7 olarak, bu iki tarafl\u0131 bir hipotez testi oldu\u011fundan ve test istatisti\u011finin mutlak de\u011feri kritik de\u011ferden k\u00fc\u00e7\u00fck oldu\u011fundan s\u0131f\u0131r hipotezi reddedilmez, 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-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> Ortalamalardaki fark i\u00e7in hipotez testi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Ortalamalar aras\u0131ndaki fark hipotez testi,<\/strong> iki pop\u00fclasyonun ortalamalar\u0131n\u0131n ayn\u0131 oldu\u011funu belirten s\u0131f\u0131r hipotezini reddetmek veya kabul etmek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> Dolay\u0131s\u0131yla, iki ortalaman\u0131n fark\u0131na ili\u015fkin bir hipotez testinin s\u0131f\u0131r hipotezi her zaman 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-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> Alternatif hipotez a\u015fa\u011f\u0131daki \u00fc\u00e7ten biri olabilir:<\/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> Daha sonra, <strong>varyans bilindi\u011finde ortalamalar aras\u0131ndaki farka ili\u015fkin hipotez testi istatisti\u011fini hesaplamak i\u00e7in form\u00fcl<\/strong> \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-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\"> 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-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-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> pop\u00fclasyon 1&#8217;in varyans\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-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> pop\u00fclasyon 2&#8217;nin varyans\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> \u00d6te yandan, <strong>varyans\u0131n bilinmedi\u011fi durumlarda ortalamalar aras\u0131ndaki farka ili\u015fkin hipotez testi istatisti\u011fini hesaplama form\u00fcl\u00fc<\/strong> \u015fu \u015fekildedir:<\/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\"> 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> varyans\u0131 bilinmeyen iki ortalaman\u0131n fark\u0131na ili\u015fkin hipotez test istatisti\u011fi olup, \u00d6\u011frenci t da\u011f\u0131l\u0131m\u0131n\u0131 takip eder.<\/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-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> \u00f6rnek 1&#8217;in varyans\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-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> \u00f6rnek 2&#8217;nin varyans\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","protected":false},"excerpt":{"rendered":"<p>Bu makale istatistikte ortalamaya ili\u015fkin hipotez testinin ne oldu\u011funu a\u00e7\u0131klamaktad\u0131r. B\u00f6ylece ortalama i\u00e7in hipotez testi form\u00fcl\u00fcn\u00fc ve ayr\u0131ca ad\u0131m ad\u0131m \u00e7\u00f6z\u00fclen bir al\u0131\u015ft\u0131rmay\u0131 bulacaks\u0131n\u0131z. Ortalama i\u00e7in hipotez testi nedir? Ortalama i\u00e7in hipotez testi, bir pop\u00fclasyon ortalamas\u0131n\u0131n s\u0131f\u0131r hipotezini reddetmek veya reddetmek i\u00e7in kullan\u0131lan istatistiksel bir y\u00f6ntemdir. Daha spesifik olarak, ortalama i\u00e7in hipotez testi, test istatisti\u011finin [&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-261","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 Ortalama i\u00e7in hipotez testi<\/title>\n<meta name=\"description\" content=\"Burada ortalamaya y\u00f6nelik hipotez testinin ne oldu\u011funu, form\u00fcl\u00fcn\u00fc ve ortalamaya y\u00f6nelik hipotez testinin somut bir \u00f6rne\u011fini bulacaks\u0131n\u0131z.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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