{"id":3296,"date":"2023-07-18T05:39:53","date_gmt":"2023-07-18T05:39:53","guid":{"rendered":"https:\/\/statorials.org\/tr\/ornek-z-testi\/"},"modified":"2023-07-18T05:39:53","modified_gmt":"2023-07-18T05:39:53","slug":"ornek-z-testi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ornek-z-testi\/","title":{"rendered":"Bir z testi \u00f6rne\u011fi: tan\u0131m, form\u00fcl ve \u00f6rnek"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Pop\u00fclasyon ortalamas\u0131n\u0131n belirli bir de\u011ferden k\u00fc\u00e7\u00fck, b\u00fcy\u00fck veya ona e\u015fit olup olmad\u0131\u011f\u0131n\u0131 test etmek i\u00e7in <strong>tek \u00f6rnekli z testi<\/strong> kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu test pop\u00fclasyon standart sapmas\u0131n\u0131n bilindi\u011fini varsayar.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde a\u015fa\u011f\u0131dakiler a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Bir numune \u00fczerinde az testi ger\u00e7ekle\u015ftirme form\u00fcl\u00fc.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Tek \u00f6rnekli z testinin varsay\u0131mlar\u0131.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bir \u00f6rnek \u00fczerinde az testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin bir \u00f6rnek.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Hadi gidelim!<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Z testi \u00f6rne\u011fi: form\u00fcl<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Tek \u00f6rnekli z testi her zaman a\u015fa\u011f\u0131daki bo\u015f ve alternatif hipotezlerden birini kullan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u0130ki kuyruklu Z testi<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03bc = \u03bc <sub>0<\/sub> (pop\u00fclasyon ortalamas\u0131 varsay\u0131msal bir \u03bc <sub>0<\/sub> de\u011ferine e\u015fittir)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> :<\/strong> \u03bc \u2260 \u03bc <sub>0<\/sub> (pop\u00fclasyon ortalamas\u0131, varsay\u0131msal bir \u03bc <sub>0<\/sub> de\u011ferine e\u015fit de\u011fildir)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>2. Sol Z testi<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03bc \u2265 \u03bc <sub>0<\/sub> (pop\u00fclasyon ortalamas\u0131, \u03bc <sub>0<\/sub> varsay\u0131msal de\u011ferinden b\u00fcy\u00fck veya ona e\u015fittir)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> :<\/strong> \u03bc &lt; \u03bc <sub>0<\/sub> (pop\u00fclasyon ortalamas\u0131 varsay\u0131msal bir de\u011ferden k\u00fc\u00e7\u00fckt\u00fcr \u03bc <sub>0<\/sub> )<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>3. D\u00fcz kuyruklu Z testi<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03bc \u2264 \u03bc <sub>0<\/sub> (pop\u00fclasyon ortalamas\u0131, \u03bc <sub>0<\/sub> varsay\u0131msal de\u011ferinden k\u00fc\u00e7\u00fck veya ona e\u015fittir)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>HA<\/sub> :<\/strong> \u03bc &gt; \u03bc <sub>0<\/sub> (pop\u00fclasyon ortalamas\u0131, varsay\u0131msal bir de\u011fer olan \u03bc <sub>0&#8217;dan<\/sub> b\u00fcy\u00fckt\u00fcr)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Z testi istatisti\u011fini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>z = (<\/strong> <strong><span style=\"text-decoration: overline;\">X<\/span> \u2013 \u03bc <sub>0<\/sub> ) \/ (\u03c3\/\u221a <span style=\"text-decoration: overline;\">n<\/span> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> :<\/strong> \u00f6rnek ortalama<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03bc <sub>0<\/sub> :<\/strong> varsay\u0131msal n\u00fcfus ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u03c3:<\/strong> pop\u00fclasyon standart sapmas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Z testi istatisti\u011fine kar\u015f\u0131l\u0131k gelen p de\u011feri, se\u00e7ti\u011finiz anlaml\u0131l\u0131k d\u00fczeyinden d\u00fc\u015f\u00fckse (ortak se\u00e7enekler 0,10, 0,05 ve 0,01&#8217;dir), o zaman <a href=\"https:\/\/statorials.org\/tr\/sifir-hipotezi-ne-zaman-reddedilir\/\" target=\"_blank\" rel=\"noopener\">s\u0131f\u0131r hipotezini reddedebilirsiniz<\/a> .<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Z testi \u00f6rne\u011fi: varsay\u0131mlar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Tek \u00f6rnekli z testi sonu\u00e7lar\u0131n\u0131n ge\u00e7erli olmas\u0131 i\u00e7in a\u015fa\u011f\u0131daki varsay\u0131mlar\u0131n kar\u015f\u0131lanmas\u0131 gerekir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Veriler s\u00fcreklidir (ayr\u0131k de\u011fildir).<\/span><\/li>\n<li> <span style=\"color: #000000;\">Veriler ilgilenilen pop\u00fclasyonun <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">basit rastgele bir \u00f6rne\u011fidir<\/a> .<\/span><\/li>\n<li> <span style=\"color: #000000;\">Pop\u00fclasyondaki veriler <a href=\"https:\/\/statorials.org\/tr\/normallik-hipotezi\/\" target=\"_blank\" rel=\"noopener\">yakla\u015f\u0131k olarak normal da\u011f\u0131l\u0131ma<\/a> sahiptir.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Pop\u00fclasyon standart sapmas\u0131 bilinmektedir.<\/span><\/li>\n<\/ul>\n<h2> <span style=\"color: #000000;\"><strong>A&#8217;dan Z&#8217;ye test \u00f6rne\u011fi<\/strong> <strong>: \u00f6rnek<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Bir pop\u00fclasyonun IQ&#8217;sunun ortalama \u03bc = 100 ve standart sapman\u0131n \u03c3 = 15 olacak \u015fekilde normal \u015fekilde da\u011f\u0131ld\u0131\u011f\u0131n\u0131 varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir bilim adam\u0131, yeni bir ilac\u0131n IQ seviyelerini etkileyip etkilemedi\u011fini bilmek istiyor. Bu y\u00fczden bunu bir ay boyunca kullanmak \u00fczere 20 hastay\u0131 i\u015fe al\u0131yor ve ay sonunda IQ seviyelerini kaydediyor:<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunu test etmek i\u00e7in a\u015fa\u011f\u0131daki ad\u0131mlar\u0131 kullanarak \u03b1 = 0,05 anlaml\u0131l\u0131k d\u00fczeyinde tek \u00f6rnekli bir z testi ger\u00e7ekle\u015ftirecektir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 1: \u00d6rnek verileri toplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki bilgileri i\u00e7eren basit rastgele bir \u00f6rnek toplad\u0131\u011f\u0131n\u0131 varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>n<\/strong> (\u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc) = 20<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span><\/strong> (\u00f6rnek ortalama IQ) = 103,05<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 2: Varsay\u0131mlar\u0131 tan\u0131mlay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki hipotezlerle bir \u00f6rnek \u00fczerinde z testini ger\u00e7ekle\u015ftirecektir:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> u = 100<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong><sub>HA<\/sub> :<\/strong> \u03bc \u2260 100<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 3: z testi istatisti\u011fini hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z testi istatisti\u011fi \u015fu \u015fekilde hesaplan\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">z = (x \u2013 \u03bc) \/ ( <span style=\"text-decoration: overline;\">\u03c3\u221an<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">z = (103,05 \u2013 100) \/ (15\/\u221a <span style=\"text-decoration: overline;\">20<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">z = 0,90933<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 4: Z testi istatisti\u011finin p de\u011ferini hesaplay\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Z puan\u0131 &#8211; P De\u011feri hesaplay\u0131c\u0131s\u0131na g\u00f6re z = 0,90933 ile ili\u015fkili iki kuyruklu p de\u011feri <strong>0,36318&#8217;dir<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Ad\u0131m 5: Bir sonu\u00e7 \u00e7\u0131kar\u0131n.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">P de\u011feri (0,36318) anlaml\u0131l\u0131k seviyesinden (0,05) k\u00fc\u00e7\u00fck olmad\u0131\u011f\u0131ndan bilim adam\u0131 s\u0131f\u0131r hipotezini reddetme konusunda ba\u015far\u0131s\u0131z olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Yeni ilac\u0131n IQ d\u00fczeylerini \u00f6nemli \u00f6l\u00e7\u00fcde etkiledi\u011fini s\u00f6yleyecek yeterli kan\u0131t yok.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Not:<\/strong> Bu tek \u00f6rnekli z testinin tamam\u0131n\u0131 Tek \u00d6rnekli Z Testi Hesaplay\u0131c\u0131s\u0131n\u0131 kullanarak da ger\u00e7ekle\u015ftirebilirsiniz.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde farkl\u0131 istatistiksel yaz\u0131l\u0131mlar kullan\u0131larak \u00f6rnek bir z testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/excelde-z-testi\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de Z Testleri Nas\u0131l Ger\u00e7ekle\u015ftirilir<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/rde-z-testi\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de Z testleri nas\u0131l yap\u0131l\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/z-testi-pitonu\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da Z Testleri Nas\u0131l Ger\u00e7ekle\u015ftirilir<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pop\u00fclasyon ortalamas\u0131n\u0131n belirli bir de\u011ferden k\u00fc\u00e7\u00fck, b\u00fcy\u00fck veya ona e\u015fit olup olmad\u0131\u011f\u0131n\u0131 test etmek i\u00e7in tek \u00f6rnekli z testi kullan\u0131l\u0131r. Bu test pop\u00fclasyon standart sapmas\u0131n\u0131n bilindi\u011fini varsayar. Bu e\u011fitimde a\u015fa\u011f\u0131dakiler a\u00e7\u0131klanmaktad\u0131r: Bir numune \u00fczerinde az testi ger\u00e7ekle\u015ftirme form\u00fcl\u00fc. Tek \u00f6rnekli z testinin varsay\u0131mlar\u0131. Bir \u00f6rnek \u00fczerinde az testinin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin bir \u00f6rnek. Hadi gidelim! [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-3296","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u00d6rnek Z Testi: Tan\u0131m, Form\u00fcl ve \u00d6rnek \u2013 Statoryaller<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde bir tan\u0131m, form\u00fcl ve tam \u00f6rnek dahil olmak \u00fczere \u00f6rnek z testine bir giri\u015f sa\u011flanmaktad\u0131r.\" \/>\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\/ornek-z-testi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u00d6rnek Z Testi: Tan\u0131m, Form\u00fcl ve \u00d6rnek \u2013 Statoryaller\" \/>\n<meta property=\"og:description\" content=\"Bu e\u011fitimde bir tan\u0131m, form\u00fcl ve tam \u00f6rnek dahil olmak \u00fczere \u00f6rnek z testine bir giri\u015f sa\u011flanmaktad\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/ornek-z-testi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-18T05:39:53+00:00\" \/>\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=\"3 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/ornek-z-testi\/\",\"url\":\"https:\/\/statorials.org\/tr\/ornek-z-testi\/\",\"name\":\"\u00d6rnek Z Testi: Tan\u0131m, Form\u00fcl ve \u00d6rnek \u2013 Statoryaller\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-18T05:39:53+00:00\",\"dateModified\":\"2023-07-18T05:39:53+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu e\u011fitimde bir tan\u0131m, form\u00fcl ve tam \u00f6rnek dahil olmak \u00fczere \u00f6rnek z testine bir giri\u015f sa\u011flanmaktad\u0131r.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/ornek-z-testi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/ornek-z-testi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/ornek-z-testi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Bir z testi \u00f6rne\u011fi: tan\u0131m, form\u00fcl ve \u00f6rnek\"}]},{\"@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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