{"id":724,"date":"2023-07-28T23:38:08","date_gmt":"2023-07-28T23:38:08","guid":{"rendered":"https:\/\/statorials.org\/tr\/ortalama-guven-araligi\/"},"modified":"2023-07-28T23:38:08","modified_gmt":"2023-07-28T23:38:08","slug":"ortalama-guven-araligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/ortalama-guven-araligi\/","title":{"rendered":"Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Bir ortalama 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;\">Bu e\u011fitimde a\u015fa\u011f\u0131dakiler a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Ortalama i\u00e7in bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturma motivasyonu.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131 olu\u015fturma form\u00fcl\u00fc.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131na dair bir \u00f6rnek.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131 nas\u0131l yorumlan\u0131r?<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131: motivasyon<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir ortalama i\u00e7in <a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener\">bir g\u00fcven aral\u0131\u011f\u0131<\/a> bile olu\u015fturmak istememizin nedeni, bir n\u00fcfus ortalamas\u0131n\u0131 tahmin ederken belirsizli\u011fimizi yakalamak istememizdir.<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin Florida&#8217;daki belirli bir kaplumba\u011fa t\u00fcr\u00fcn\u00fcn ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 tahmin etmek istedi\u011fimizi varsayal\u0131m. Florida&#8217;da binlerce kaplumba\u011fa oldu\u011fundan, etrafta dola\u015f\u0131p her kaplumba\u011fay\u0131 ayr\u0131 ayr\u0131 tartmak son derece zaman al\u0131c\u0131 ve pahal\u0131 olacakt\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bunun yerine, 50 kaplumba\u011fadan olu\u015fan <a href=\"https:\/\/statorials.org\/tr\/ornekleme-yontemleri\/\" target=\"_blank\" rel=\"noopener\">basit bir rastgele \u00f6rnek<\/a> alabilir ve ger\u00e7ek pop\u00fclasyon ortalamas\u0131n\u0131 tahmin etmek i\u00e7in bu \u00f6rnekteki kaplumba\u011falar\u0131n ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 kullanabiliriz:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-7353 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cimoyenne1.png\" alt=\"\u00d6rnek bir pop\u00fclasyon \u00f6rne\u011fi\" width=\"405\" height=\"270\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Sorun, numunenin ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n t\u00fcm pop\u00fclasyonun ortalama a\u011f\u0131rl\u0131\u011f\u0131yla tam olarak e\u015fle\u015fece\u011finin garanti edilememesidir. Dolay\u0131s\u0131yla, bu belirsizli\u011fi yakalamak i\u00e7in pop\u00fclasyondaki kaplumba\u011falar\u0131n ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 i\u00e7ermesi muhtemel bir dizi de\u011fer i\u00e7eren bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturabiliriz.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131: form\u00fcl<\/strong><\/span><\/h3>\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 =<\/strong> <strong><span style=\"text-decoration: overline;\">x<\/span> +\/- z*(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>z:<\/strong> se\u00e7ilen z 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;\">Kulland\u0131\u011f\u0131n\u0131z z de\u011feri se\u00e7ti\u011finiz g\u00fcven d\u00fczeyine ba\u011fl\u0131d\u0131r. A\u015fa\u011f\u0131daki tabloda en yayg\u0131n g\u00fcven d\u00fczeyi se\u00e7eneklerine kar\u015f\u0131l\u0131k gelen z de\u011feri g\u00f6sterilmektedir:<\/span><\/p>\n<table>\n<tbody>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>Bir g\u00fcven d\u00fczeyi<\/strong><\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>z de\u011feri<\/strong><\/span><\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,90<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1.645<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,95<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">1.96<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">0,99<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">2.58<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: left;\"> <span style=\"color: #000000;\">Daha y\u00fcksek g\u00fcven d\u00fczeylerinin daha b\u00fcy\u00fck z de\u011ferlerine kar\u015f\u0131l\u0131k geldi\u011fini ve bunun da daha geni\u015f g\u00fcven aral\u0131klar\u0131na yol a\u00e7t\u0131\u011f\u0131n\u0131 unutmay\u0131n. Bu, \u00f6rne\u011fin ayn\u0131 veri seti i\u00e7in %99 g\u00fcven aral\u0131\u011f\u0131n\u0131n %95 g\u00fcven aral\u0131\u011f\u0131ndan daha geni\u015f olaca\u011f\u0131 anlam\u0131na gelir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131: \u00f6rnek<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki bilgileri i\u00e7eren rastgele bir kaplumba\u011fa \u00f6rne\u011fi toplad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc <strong>n = 25<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama numune a\u011f\u0131rl\u0131\u011f\u0131 <strong><span style=\"text-decoration: overline;\">x<\/span> = 300<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem standart sapmas\u0131 <strong>s = 18,5<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">N\u00fcfusun ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131 i\u00e7in farkl\u0131 g\u00fcven aral\u0131klar\u0131n\u0131 nas\u0131l bulaca\u011f\u0131n\u0131z a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%90 g\u00fcven aral\u0131\u011f\u0131:<\/strong> 300 +\/- 1,645*(18,5\/\u221a <span style=\"text-decoration: overline;\">25<\/span> ) = <strong>[293,91, 306,09]<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%95 g\u00fcven aral\u0131\u011f\u0131:<\/strong> 300 +\/- 1,96*(18,5\/\u221a <span style=\"text-decoration: overline;\">25<\/span> ) = <strong>[292,75, 307,25]<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>%99 g\u00fcven aral\u0131\u011f\u0131:<\/strong> 300 +\/- 2,58*(18,5\/\u221a <span style=\"text-decoration: overline;\">25<\/span> ) = [ <b><span id=\"low90\">290,47<\/span> , <span id=\"high90\">309,53]<\/span><\/b><\/span><\/p>\n<p> <em><span style=\"color: #000000;\"><strong>Not:<\/strong> Bu g\u00fcven aral\u0131klar\u0131n\u0131 \u0130statistiksel G\u00fcven Aral\u0131\u011f\u0131 Hesaplay\u0131c\u0131s\u0131n\u0131 kullanarak da bulabilirsiniz.<\/span><\/em><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131: yorumlama<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Bir g\u00fcven aral\u0131\u011f\u0131n\u0131 yorumlama \u015feklimiz \u015fu \u015fekildedir:<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\">[292,75, 307,25] g\u00fcven aral\u0131\u011f\u0131n\u0131n kaplumba\u011fa pop\u00fclasyonunun ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131 i\u00e7erme olas\u0131l\u0131\u011f\u0131 %95&#8217;tir.<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\">Ayn\u0131 \u015feyi s\u00f6ylemenin ba\u015fka bir yolu da, ger\u00e7ek n\u00fcfus ortalamas\u0131n\u0131n %95 g\u00fcven aral\u0131\u011f\u0131n\u0131n d\u0131\u015f\u0131nda olma ihtimalinin yaln\u0131zca %5 oldu\u011fudur. Yani, kaplumba\u011fa pop\u00fclasyonunun ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131n\u0131n 307,25 pounddan fazla veya 292,75 pounddan az olma ihtimali yaln\u0131zca %5&#8217;tir.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131, belirli bir g\u00fcven d\u00fczeyine sahip bir pop\u00fclasyon ortalamas\u0131n\u0131 i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\u0131r. Bu e\u011fitimde a\u015fa\u011f\u0131dakiler a\u00e7\u0131klanmaktad\u0131r: Ortalama i\u00e7in bir g\u00fcven aral\u0131\u011f\u0131 olu\u015fturma motivasyonu. Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131 olu\u015fturma form\u00fcl\u00fc. Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131na dair bir \u00f6rnek. Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131 nas\u0131l yorumlan\u0131r? Ortalama i\u00e7in [&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-724","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>Ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131 - Statorials<\/title>\n<meta name=\"description\" content=\"Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131na ili\u015fkin, ad\u0131m ad\u0131m \u00f6rnek i\u00e7eren basit bir a\u00e7\u0131klama.\" \/>\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\/ortalama-guven-araligi\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131 - Statorials\" \/>\n<meta property=\"og:description\" content=\"Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131na ili\u015fkin, ad\u0131m ad\u0131m \u00f6rnek i\u00e7eren basit bir a\u00e7\u0131klama.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/ortalama-guven-araligi\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-28T23:38:08+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/cimoyenne1.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=\"3 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/ortalama-guven-araligi\/\",\"url\":\"https:\/\/statorials.org\/tr\/ortalama-guven-araligi\/\",\"name\":\"Ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131 - Statorials\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-28T23:38:08+00:00\",\"dateModified\":\"2023-07-28T23:38:08+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l olu\u015fturulaca\u011f\u0131na ili\u015fkin, ad\u0131m ad\u0131m \u00f6rnek i\u00e7eren basit bir a\u00e7\u0131klama.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/ortalama-guven-araligi\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/ortalama-guven-araligi\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/ortalama-guven-araligi\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131\"}]},{\"@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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