{"id":3810,"date":"2023-07-15T10:15:03","date_gmt":"2023-07-15T10:15:03","guid":{"rendered":"https:\/\/statorials.org\/tr\/s-sqrt-n\/"},"modified":"2023-07-15T10:15:03","modified_gmt":"2023-07-15T10:15:03","slug":"s-sqrt-n","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/s-sqrt-n\/","title":{"rendered":"I\u0307statistiklerde s\/sqrt(n) ne zaman kullan\u0131l\u0131r?"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u0130statistiklerde <strong>s\/ <span style=\"text-decoration: overline;\">\u221an<\/span><\/strong> form\u00fcl\u00fcyle farkl\u0131 senaryolarda kar\u015f\u0131la\u015f\u0131rs\u0131n\u0131z.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu form\u00fcl \u00f6rnek ortalaman\u0131n standart hatas\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Form\u00fclde <strong>s<\/strong> \u00f6rneklem standart sapmas\u0131n\u0131, <strong>n<\/strong> ise \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc temsil etmektedir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu form\u00fcl iki istatistiksel testin hesaplanmas\u0131nda g\u00f6r\u00fcn\u00fcr:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> \u00d6rnek bir t testi<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> Ana k\u00fctle ortalamas\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler bu iki senaryoda <strong>s\/\u221a <span style=\"text-decoration: overline;\">n&#8217;nin<\/span><\/strong> nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Tek \u00f6rnekli t testinde s \/ sqrt(n) i\u015flevini kullanma<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\"><strong>Tek \u00f6rnekli t testi,<\/strong> bir <a href=\"https:\/\/statorials.org\/tr\/populasyon-ve-ornek\/\" target=\"_blank\" rel=\"noopener\">pop\u00fclasyonun<\/a> ortalamas\u0131n\u0131n belirli bir de\u011fere e\u015fit olup olmad\u0131\u011f\u0131n\u0131 test etmek i\u00e7in kullan\u0131l\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">T-testi istatisti\u011fini hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">t = ( <span style=\"text-decoration: overline;\">X<\/span> \u2013 \u03bc) \/ (s\/ <span style=\"text-decoration: overline;\">\u221an<\/span> )<\/span><\/strong><\/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>s:<\/strong> numune 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;\">\u00d6rne\u011fin, belirli bir pop\u00fclasyondaki kaplumba\u011falar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 300 pound&#8217;a e\u015fit olup olmad\u0131\u011f\u0131n\u0131 test etmek istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki bilgileri i\u00e7eren <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">basit ve rastgele bir kaplumba\u011fa \u00f6rne\u011fi<\/a> topluyoruz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc n = 40<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama numune a\u011f\u0131rl\u0131\u011f\u0131 <span style=\"text-decoration: overline;\">x<\/span> = 300<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem standart sapmas\u0131 s = 18,5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Tek \u00f6rnek t-testini a\u015fa\u011f\u0131daki hipotezlerle ger\u00e7ekle\u015ftirece\u011fiz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u03bc = 310 (N\u00fcfus ortalamas\u0131 310 kitaba e\u015fittir)<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub> :<\/strong> \u03bc \u2260 310 (n\u00fcfus ortalamas\u0131 310 pound&#8217;a e\u015fit de\u011fildir)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0130lk olarak test istatisti\u011fini hesaplayaca\u011f\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\">t = ( <span style=\"text-decoration: overline;\">x<\/span> \u2013 \u03bc) \/ (s\/ <span style=\"text-decoration: overline;\">\u221an<\/span> ) = (300-310) \/ (18,5\/ <span style=\"text-decoration: overline;\">\u221a40<\/span> ) = -3,4187<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/t-puani-p-degeri-hesaplayicisi\/\" target=\"_blank\" rel=\"noopener\">P De\u011feri hesaplay\u0131c\u0131s\u0131na g\u00f6re T puan\u0131<\/a> , t = -3,4817 ve serbestlik derecesi = n-1 = 40-1 = 39 ile ili\u015fkili p de\u011feri 0,00149&#8217;dur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu p de\u011feri 0,05&#8217;ten k\u00fc\u00e7\u00fck oldu\u011fundan s\u0131f\u0131r hipotezini reddediyoruz. Bu kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 310 pounda e\u015fit olmad\u0131\u011f\u0131n\u0131 s\u00f6yleyecek yeterli kan\u0131t\u0131m\u0131z var.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Pop\u00fclasyon ortalamas\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131nda s \/ sqrt(n) i\u015flevini kullanma<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\"><strong>Bir pop\u00fclasyon ortalamas\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131,<\/strong> belirli bir g\u00fcven d\u00fczeyine sahip bir pop\u00fclasyon ortalamas\u0131n\u0131 i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bir ortalaman\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 = <span style=\"text-decoration: overline;\">x<\/span> +\/- t <sub>n-1, 1-\u03b1\/2<\/sub> *(s\/\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>t:<\/strong> t-kritik de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> numune 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;\">\u00d6rne\u011fin, belirli bir pop\u00fclasyondaki kaplumba\u011falar\u0131n ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131 i\u00e7in bir g\u00fcven aral\u0131\u011f\u0131 hesaplamak istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki bilgileri i\u00e7eren basit ve rastgele bir kaplumba\u011fa \u00f6rne\u011fi topluyoruz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc n = 40<\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama numune a\u011f\u0131rl\u0131\u011f\u0131 <span style=\"text-decoration: overline;\">x<\/span> = 300<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem standart sapmas\u0131 s = 18,5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Kaplumba\u011fa pop\u00fclasyonunun ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131na ili\u015fkin %95 g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullanabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">%95 GA = <span style=\"text-decoration: overline;\">x<\/span> +\/- t <sub>n-1, 1-\u03b1\/2<\/sub> *(s\/\u221a <span style=\"text-decoration: overline;\">n<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\"><span style=\"color: #000000;\">%95 GA = 300 +\/- (2,022691) * (18,5\/\u221a <span style=\"text-decoration: overline;\">40<\/span> )<\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\">%95 GA = [294,083, 305,917]<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Kaplumba\u011fa pop\u00fclasyonunun ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 294.083 pound ile 305.917 pound aras\u0131ndad\u0131r.<\/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\u011fitimler, farkl\u0131 yaz\u0131l\u0131mlarda bir ortalaman\u0131n standart hatas\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 a\u00e7\u0131klamaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/excel-standart-hatasi\/\" target=\"_blank\" rel=\"noopener\">Excel&#8217;de Ortalaman\u0131n Standart Hatas\u0131 Nas\u0131l Hesaplan\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/ortalama-rnin-standart-hatasi\/\" target=\"_blank\" rel=\"noopener\">R cinsinden ortalaman\u0131n standart hatas\u0131 nas\u0131l hesaplan\u0131r?<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/python-ortalamasinin-standart-hatasi\/\" target=\"_blank\" rel=\"noopener\">Python&#8217;da ortalaman\u0131n standart hatas\u0131 nas\u0131l hesaplan\u0131r<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130statistiklerde s\/ \u221an form\u00fcl\u00fcyle farkl\u0131 senaryolarda kar\u015f\u0131la\u015f\u0131rs\u0131n\u0131z. Bu form\u00fcl \u00f6rnek ortalaman\u0131n standart hatas\u0131n\u0131 hesaplamak i\u00e7in kullan\u0131l\u0131r. Form\u00fclde s \u00f6rneklem standart sapmas\u0131n\u0131, n ise \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc temsil etmektedir. Bu form\u00fcl iki istatistiksel testin hesaplanmas\u0131nda g\u00f6r\u00fcn\u00fcr: 1. \u00d6rnek bir t testi 2. Ana k\u00fctle ortalamas\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131 A\u015fa\u011f\u0131daki \u00f6rnekler bu iki senaryoda s\/\u221a n&#8217;nin nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 [&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-3810","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>\u0130statistiklerde s\/sqrt(n) ne zaman kullan\u0131l\u0131r? - Statorials<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde s\/sqrt(n) form\u00fcl\u00fcn\u00fcn istatistikte ne zaman kullan\u0131laca\u011f\u0131 \u00e7e\u015fitli \u00f6rneklerle a\u00e7\u0131klanmaktad\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\/s-sqrt-n\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0130statistiklerde s\/sqrt(n) ne zaman kullan\u0131l\u0131r? - Statorials\" \/>\n<meta property=\"og:description\" content=\"Bu e\u011fitimde s\/sqrt(n) form\u00fcl\u00fcn\u00fcn istatistikte ne zaman kullan\u0131laca\u011f\u0131 \u00e7e\u015fitli \u00f6rneklerle a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/s-sqrt-n\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-15T10:15:03+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\/s-sqrt-n\/\",\"url\":\"https:\/\/statorials.org\/tr\/s-sqrt-n\/\",\"name\":\"\u0130statistiklerde s\/sqrt(n) ne zaman kullan\u0131l\u0131r? - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-15T10:15:03+00:00\",\"dateModified\":\"2023-07-15T10:15:03+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu e\u011fitimde s\/sqrt(n) form\u00fcl\u00fcn\u00fcn istatistikte ne zaman kullan\u0131laca\u011f\u0131 \u00e7e\u015fitli \u00f6rneklerle a\u00e7\u0131klanmaktad\u0131r.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/s-sqrt-n\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/s-sqrt-n\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/s-sqrt-n\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"I\u0307statistiklerde s\/sqrt(n) ne zaman kullan\u0131l\u0131r?\"}]},{\"@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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