{"id":289,"date":"2023-08-03T01:52:23","date_gmt":"2023-08-03T01:52:23","guid":{"rendered":"https:\/\/statorials.org\/tr\/z-testi\/"},"modified":"2023-08-03T01:52:23","modified_gmt":"2023-08-03T01:52:23","slug":"z-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/z-testi\/","title":{"rendered":"Z testi"},"content":{"rendered":"<p>Bu makalede istatistikte Z testinin ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Bu nedenle Z testinin nas\u0131l yap\u0131laca\u011f\u0131n\u0131, farkl\u0131 Z testi form\u00fcllerini ve son olarak Z testi ile di\u011fer istatistiksel testler aras\u0131ndaki fark\u0131 ke\u015ffedeceksiniz.<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-una-prueba-z\"><\/span>Z testi nedir?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> \u0130statistikte <strong>Z testi<\/strong> , test istatisti\u011fi normal bir da\u011f\u0131l\u0131m izledi\u011finde kullan\u0131lan bir hipotez testidir. Z testinden elde edilen istatisti\u011fe Z istatisti\u011fi veya Z de\u011feri denir.<\/p>\n<p> Z testi form\u00fcl\u00fc her zaman ayn\u0131d\u0131r, daha do\u011frusu Z testi istatisti\u011fi, hesaplanan \u00f6rnek de\u011feri ile \u00f6nerilen pop\u00fclasyon de\u011feri aras\u0131ndaki fark\u0131n, pop\u00fclasyon parametresinin standart sapmas\u0131na b\u00f6l\u00fcnmesine e\u015fittir.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5ad1fab5e2c6a8d32ae02f2e2d16d42c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Z=\\cfrac{\\widehat{X}-X}{\\sigma_{_X}}\" title=\"Rendered by QuickLaTeX.com\" height=\"49\" width=\"92\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Z testi, test istatisti\u011finin normal bir da\u011f\u0131l\u0131m izledi\u011fi hipotez testlerinin s\u0131f\u0131r hipotezini reddetmek veya kabul etmek i\u00e7in kullan\u0131l\u0131r.<\/p>\n<p> \u00d6rne\u011fin, Z testi, pop\u00fclasyon varyans\u0131 bilindi\u011finde, pop\u00fclasyon ortalamas\u0131n\u0131n de\u011feri hakk\u0131ndaki bir hipotezi reddetmek veya kabul etmek i\u00e7in ortalaman\u0131n hipotezini test etmek i\u00e7in kullan\u0131l\u0131r. <\/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\/hipotez-testi-1\/\">Hipotez testi nedir?<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"tipos-de-pruebas-z\"><\/span> Z testi t\u00fcrleri<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Hipotez testinin ger\u00e7ekle\u015ftirildi\u011fi parametreye ba\u011fl\u0131 olarak farkl\u0131 Z testi t\u00fcrleri ay\u0131rt edilebilir:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Ortalama i\u00e7in Z testi.<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Orant\u0131 i\u00e7in Z testi.<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Ortalamalardaki fark i\u00e7in Z testi.<\/strong><\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Oranlardaki fark i\u00e7in Z testi.<\/strong><\/span><\/li>\n<\/ul>\n<p> A\u015fa\u011f\u0131da her Z testi t\u00fcr\u00fcne ait form\u00fcl\u00fc g\u00f6rebilirsiniz.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-media\"><\/span> Ortalama i\u00e7in Z testi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Ortalama i\u00e7in Z testi 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 Z 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> Z testinin kritik de\u011ferleri standart normal da\u011f\u0131l\u0131m tablosundan elde edilir. <\/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\/ortalama-icin-hipotez-testi\/\">Ortalama i\u00e7in hipotez testi<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-proporcion\"><\/span> Oran i\u00e7in Z testi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Oran i\u00e7in Z testi 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-e2f5ad36dae72cd89279809ab3ea6d20_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\widehat{p}-p}{\\displaystyle\\sqrt{\\frac{p(1-p)}{n}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"67\" width=\"123\" style=\"vertical-align: -41px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> 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> orant\u0131 i\u00e7in Z 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-ecd29d136a62fc6b274e1181e064e20e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00f6rnek oran\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-5faad0904f612a3fa5b27faafb8dc903_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00f6nerilen oran\u0131n de\u011feridir.<\/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<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-661a2bbf8dccd197bcf450330420cbc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\sqrt{\\frac{p(1-p)}{n}}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"84\" style=\"vertical-align: -13px;\"><\/p>\n<p> oran\u0131n standart sapmas\u0131d\u0131r.<\/li>\n<\/ul>\n<p> Oran i\u00e7in Z testi istatisti\u011fini hesaplaman\u0131n yeterli olmad\u0131\u011f\u0131n\u0131, daha sonra elde edilen sonucu yorumlaman\u0131z gerekti\u011fini unutmay\u0131n:<\/p>\n<ul style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">Oran 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;\">Oran i\u00e7in hipotez testi sa\u011f kuyrukla e\u015fle\u015firse, 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;\">Oran i\u00e7in hipotez testi sol kuyrukla e\u015fle\u015firse, istatisti\u011fin -Z <sub>\u03b1<\/sub> kritik de\u011ferinden k\u00fc\u00e7\u00fck olmas\u0131 durumunda 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-7d5bd583532769e3014286e8ffd94c9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l}H_1: p\\neq p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } |Z|>Z_{\\alpha\/2} \\text{ se rechaza } H_0\\\\[3ex]H_1: p> p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z>Z_{\\alpha} \\text{ se rechaza } H_0\\\\[3ex]H_1: p< p_0 \\ \\color{orange}\\bm{\\longrightarrow}\\color{black} \\ \\text{Si } Z<-Z_{\\alpha} \\text{ se rechaza } H_0\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"437\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 20px; padding-left: 30px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Bak\u0131n\u0131z:<\/strong> <a href=\"https:\/\/statorials.org\/tr\/oranti-icin-hipotez-testi\/\">Oran i\u00e7in hipotez testi<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-diferencia-de-medias\"><\/span> Ortalamalardaki fark i\u00e7in Z testi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> <strong>Ortalamalardaki fark i\u00e7in Z testi istatisti\u011fini hesaplama 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-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\u0131na y\u00f6nelik Z 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-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<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-arasindaki-farka-yonelik-hipotez-testi\/\">Ortalamalar aras\u0131ndaki fark i\u00e7in hipotez testi<\/a> <\/div>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-para-la-diferencia-de-proporciones\"><\/span> Oranlardaki fark i\u00e7in Z testi<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> \u0130ki pop\u00fclasyonun <strong>oranlar\u0131ndaki farka ili\u015fkin Z testi istatisti\u011fini hesaplama 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-161267e1562535b8ded23017389e0807_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle Z=\\frac{\\displaystyle (\\widehat{p_1}-\\widehat{p_2})-(p_1-p_2)}{\\displaystyle \\sqrt{p_0(1-p_0)\\left(\\frac{1}{n_1}+\\frac{1}{n_2}\\right)}}\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"229\" style=\"vertical-align: -52px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> 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> oranlardaki fark i\u00e7in Z 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-023bcfb3fa329ff4f481163d36b65bf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p> n\u00fcfus oran\u0131 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-1a0ac2d00900c29ac35c13956874c642_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> n\u00fcfus oran\u0131 2&#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-a4c76b176c372799a3a3a7aa8858eecf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_1}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"16\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00f6rnek 1&#8217;in oran\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-cd7916af5298a603fad64ab8fb2501a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\widehat{p_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00f6rnek oran\u0131 2&#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-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<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ccd892ed2f60029f47331cf785d30482_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_0\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: -4px;\"><\/p>\n<p> iki numunenin birle\u015fik oran\u0131d\u0131r.<\/li>\n<\/ul>\n<p> \u0130ki numunenin birle\u015fik oran\u0131 a\u015fa\u011f\u0131daki \u015fekilde 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-6f349422474d622468a6a14f445f2eb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p_0=\\cfrac{x_1+x_2}{n_1+n_2}\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"102\" style=\"vertical-align: -15px;\"><\/p>\n<\/p>\n<p> Alt\u0131n<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dad27a9703483183e1afd245f5232b83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rnekteki sonu\u00e7lar\u0131n say\u0131s\u0131 iy<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5f087375b50e0b49186779714206626b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc i&#8217;dir. <\/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\/oranlardaki-fark-icin-hipotez-testi\/\">Oranlardaki fark i\u00e7in hipotez testi<\/a><\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hacer-una-prueba-z\"><\/span>Z testi nas\u0131l yap\u0131l\u0131r<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Art\u0131k farkl\u0131 Z testi form\u00fcllerinin neler oldu\u011funu g\u00f6rd\u00fc\u011f\u00fcm\u00fcze g\u00f6re, Z testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine bakal\u0131m.<\/p>\n<p> Z testi ger\u00e7ekle\u015ftirme ad\u0131mlar\u0131 a\u015fa\u011f\u0131daki gibidir.<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Hipotez testinin <a href=\"https:\/\/statorials.org\/tr\/bos-ve-alternatif-hipotez\/\">bo\u015f hipotezini ve alternatif hipotezini<\/a> tan\u0131mlay\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Hipotez testinin <a href=\"https:\/\/statorials.org\/tr\/onem-duzeyi\/\">alfa (\u03b1) anlaml\u0131l\u0131k d\u00fczeyine<\/a> karar verin.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Z testinin kullan\u0131m\u0131na ili\u015fkin gereksinimlerin kar\u015f\u0131land\u0131\u011f\u0131n\u0131 do\u011frulay\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">\u0130lgili Z testi form\u00fcl\u00fcn\u00fc uygulay\u0131n ve test istatisti\u011fini hesaplay\u0131n.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\">Z testi sonucunu kritik test de\u011feriyle kar\u015f\u0131la\u015ft\u0131rarak yorumlay\u0131n.<\/span><\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"prueba-z-y-prueba-t\"><\/span>Z testi ve t testi<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Son olarak Z testi ile t testi aras\u0131ndaki fark\u0131n ne oldu\u011funu g\u00f6rece\u011fiz, \u00e7\u00fcnk\u00fc bunlar kesinlikle istatistikte en \u00e7ok kullan\u0131lan iki hipotez testi t\u00fcr\u00fcd\u00fcr.<\/p>\n<p> <strong>\u00d6\u011frenci t testi<\/strong> olarak da adland\u0131r\u0131lan <strong>t testi<\/strong> , incelenen pop\u00fclasyonun normal bir da\u011f\u0131l\u0131m izledi\u011fi ancak \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn pop\u00fclasyon varyans\u0131n\u0131 bilemeyecek kadar k\u00fc\u00e7\u00fck oldu\u011fu durumlarda kullan\u0131lan bir hipotez testidir.<\/p>\n<p> Bu nedenle <strong>Z testi ile t testi aras\u0131ndaki temel fark,<\/strong> varyans\u0131n bilinip bilinmemesidir. Ana k\u00fctle varyans\u0131n\u0131n bilindi\u011fi durumlarda Z testi, ana k\u00fctle varyans\u0131n\u0131n bilinmedi\u011fi durumlarda ise t testi kullan\u0131l\u0131r. <\/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\/ogrenci-t-testi\/\">t testi (istatistikler)<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Bu makalede istatistikte Z testinin ne oldu\u011fu ve ne i\u00e7in kullan\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Bu nedenle Z testinin nas\u0131l yap\u0131laca\u011f\u0131n\u0131, farkl\u0131 Z testi form\u00fcllerini ve son olarak Z testi ile di\u011fer istatistiksel testler aras\u0131ndaki fark\u0131 ke\u015ffedeceksiniz. Z testi nedir? \u0130statistikte Z testi , test istatisti\u011fi normal bir da\u011f\u0131l\u0131m izledi\u011finde kullan\u0131lan bir hipotez testidir. Z testinden elde edilen [&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-289","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>\u25b7Z testi<\/title>\n<meta name=\"description\" content=\"Burada istatistikte Z testinin ne oldu\u011funu, Z testinin (form\u00fcl) nas\u0131l yap\u0131laca\u011f\u0131n\u0131 ve Z testinin \u00e7\u00f6z\u00fcml\u00fc \u00f6rneklerini \u00f6\u011freneceksiniz.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/tr\/z-testi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7Z testi\" \/>\n<meta property=\"og:description\" content=\"Burada istatistikte Z testinin ne oldu\u011funu, Z testinin (form\u00fcl) nas\u0131l yap\u0131laca\u011f\u0131n\u0131 ve Z testinin \u00e7\u00f6z\u00fcml\u00fc \u00f6rneklerini \u00f6\u011freneceksiniz.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/z-testi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-08-03T01:52:23+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-5ad1fab5e2c6a8d32ae02f2e2d16d42c_l3.png\" \/>\n<meta name=\"author\" content=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/z-testi\/\",\"url\":\"https:\/\/statorials.org\/tr\/z-testi\/\",\"name\":\"\u25b7Z testi\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-08-03T01:52:23+00:00\",\"dateModified\":\"2023-08-03T01:52:23+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Burada istatistikte Z testinin ne oldu\u011funu, Z testinin (form\u00fcl) nas\u0131l yap\u0131laca\u011f\u0131n\u0131 ve Z testinin \u00e7\u00f6z\u00fcml\u00fc \u00f6rneklerini \u00f6\u011freneceksiniz.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/z-testi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/z-testi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/z-testi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Z testi\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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