{"id":4910,"date":"2023-07-06T13:07:19","date_gmt":"2023-07-06T13:07:19","guid":{"rendered":"https:\/\/statorials.org\/id\/contoh-soal-interval-kepercayaan\/"},"modified":"2023-07-06T13:07:19","modified_gmt":"2023-07-06T13:07:19","slug":"contoh-soal-interval-kepercayaan","status":"publish","type":"post","link":"https:\/\/statorials.org\/id\/contoh-soal-interval-kepercayaan\/","title":{"rendered":"Cara menghitung interval keyakinan: 3 contoh soal"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Interval kepercayaan suatu mean<\/strong> adalah rentang nilai yang kemungkinan mengandung <a href=\"https:\/\/statorials.org\/id\/rata-rata-sampel-dibandingkan-dengan-rata-rata-populasi\/\" target=\"_blank\" rel=\"noopener\">mean populasi<\/a> dengan tingkat kepercayaan tertentu.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Kami menggunakan rumus berikut untuk menghitung interval kepercayaan untuk suatu mean:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Interval kepercayaan =<\/strong> <strong><span style=\"text-decoration: overline;\">x<\/span> +\/- t*(s\/\u221a <span style=\"text-decoration: overline;\">n<\/span> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Emas:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> :<\/strong> mean sampel<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>t :<\/strong> nilai kritis t<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> deviasi standar sampel<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> ukuran sampel<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Catatan<\/strong> : Kita mengganti nilai kritis dengan nilai kritis az dalam rumus jika simpangan baku populasi (\u03c3) diketahui <em>dan<\/em> ukuran sampel lebih besar dari 30.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Contoh berikut menunjukkan cara membuat interval kepercayaan untuk rata-rata dalam tiga skenario berbeda:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Deviasi standar populasi (\u03c3) tidak diketahui<\/span><\/li>\n<li> <span style=\"color: #000000;\">Simpangan baku populasi (\u03c3) diketahui tetapi n \u2264 30<\/span><\/li>\n<li> <span style=\"color: #000000;\">Simpangan baku populasi (\u03c3) diketahui dan n &gt; 30<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Ayo pergi!<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Contoh 1: selang kepercayaan ketika \u03c3 tidak diketahui<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Misalkan kita ingin menghitung interval kepercayaan 95% untuk tinggi rata-rata (dalam inci) suatu spesies tumbuhan tertentu.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Misalkan kita mengumpulkan sampel acak sederhana dengan informasi berikut:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">mean sampel ( <span style=\"text-decoration: overline;\">x<\/span> ) = 12<\/span><\/li>\n<li> <span style=\"color: #000000;\">ukuran sampel (n) = 19<\/span><\/li>\n<li> <span style=\"color: #000000;\">deviasi standar sampel (s) = 6,3<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Kita dapat menggunakan rumus berikut untuk membuat interval kepercayaan ini:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">95% CI = <span style=\"text-decoration: overline;\">x<\/span> +\/- t*(s\/\u221a <span style=\"text-decoration: overline;\">n<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">95% CI = 12 +\/- t <sub>n-1, \u03b1\/2<\/sub> *(6,3\/\u221a <span style=\"text-decoration: overline;\">19<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">95% CI = 12 +\/- t <sub>18,025<\/sub> *(6,3\/\u221a <span style=\"text-decoration: overline;\">19<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">CI 95% = 12 +\/- 2,1009*(6,3\/\u221a <span style=\"text-decoration: overline;\">19<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">CI 95% = <strong>(8.964, 15.037)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Interval kepercayaan 95% untuk tinggi populasi rata-rata spesies tumbuhan tertentu adalah <strong>(8,964 inci, 15,037 inci)<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Catatan #1<\/strong> : Kami menggunakan kalkulator distribusi t terbalik untuk mencari nilai t kritis yang terkait dengan 18 derajat kebebasan dan tingkat kepercayaan 0,95.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Catatan #2<\/strong> : Karena simpangan baku populasi (\u03c3) tidak diketahui, kami menggunakan nilai kritis t saat menghitung interval kepercayaan.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Contoh 2:<\/strong><\/span> <span style=\"color: #000000;\"><strong>Interval kepercayaan ketika \u03c3 diketahui tetapi n \u2264 30<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Misalkan kita ingin menghitung interval kepercayaan 99% untuk nilai rata-rata ujian masuk perguruan tinggi tertentu.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Misalkan kita mengumpulkan sampel acak sederhana dengan informasi berikut:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">mean sampel ( <span style=\"text-decoration: overline;\">x<\/span> ) = 85<\/span><\/li>\n<li> <span style=\"color: #000000;\">ukuran sampel (n) = 25<\/span><\/li>\n<li> <span style=\"color: #000000;\">simpangan baku populasi (\u03c3) = 3,5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Kita dapat menggunakan rumus berikut untuk membuat interval kepercayaan ini:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">99% CI = <span style=\"text-decoration: overline;\">x<\/span> +\/- t*(s\/\u221a <span style=\"text-decoration: overline;\">n<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">99% CI = 85 +\/- t <sub>n-1, \u03b1\/2<\/sub> *(3,5\/\u221a <span style=\"text-decoration: overline;\">25<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">99% CI = 85 +\/- t <sub>24,005<\/sub> *(3,5\/\u221a <span style=\"text-decoration: overline;\">25<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">CI 99% = 85 +\/- 2,7969*(3,5\/\u221a <span style=\"text-decoration: overline;\">25<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">CI 99% = <strong>(83.042, 86.958)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Interval kepercayaan 99% untuk nilai rata-rata penduduk pada ujian masuk perguruan tinggi ini adalah <strong>(83.042, 86.958)<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Catatan #1<\/strong> : Kami menggunakan kalkulator distribusi t terbalik untuk mencari nilai t kritis yang terkait dengan 24 derajat kebebasan dan tingkat kepercayaan 0,99.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Catatan #2<\/strong> : Karena simpangan baku populasi (\u03c3) diketahui tetapi ukuran sampel (n) kurang dari 30, kami menggunakan nilai kritis t saat menghitung interval kepercayaan.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Contoh 3:<\/strong><\/span> <span style=\"color: #000000;\"><strong>Interval kepercayaan ketika \u03c3 diketahui dan n &gt; 30<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Misalkan kita ingin menghitung selang kepercayaan 90% untuk berat rata-rata suatu spesies penyu tertentu.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Misalkan kita mengumpulkan sampel acak sederhana dengan informasi berikut:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">mean sampel ( <span style=\"text-decoration: overline;\">x<\/span> ) = 300<\/span><\/li>\n<li> <span style=\"color: #000000;\">ukuran sampel (n) = 40<\/span><\/li>\n<li> <span style=\"color: #000000;\">simpangan baku populasi (\u03c3) = 15<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Kita dapat menggunakan rumus berikut untuk membuat interval kepercayaan ini:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">90% CI = <span style=\"text-decoration: overline;\">x<\/span> +\/- z*(\u03c3\/\u221a <span style=\"text-decoration: overline;\">n<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">CI 90% = 300 +\/- 1,645*(15\/\u221a <span style=\"text-decoration: overline;\">40<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">CI 90% = <strong>(296.099, 303.901)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Interval kepercayaan 90% untuk bobot populasi rata-rata spesies penyu tertentu adalah <strong>(83.042, 86.958)<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Catatan #1<\/strong> : Kami menggunakan Kalkulator Nilai Z Kritis untuk mencari nilai z kritis yang terkait dengan tingkat signifikansi 0,1.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Catatan #2<\/strong> : Karena simpangan baku populasi (\u03c3) diketahui dan ukuran sampel (n) lebih besar dari 30, kami menggunakan nilai kritis z saat menghitung interval kepercayaan.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Sumber daya tambahan<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Tutorial berikut memberikan informasi tambahan tentang interval kepercayaan:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/id\/contoh-nyata-interval-kepercayaan\/\" target=\"_blank\" rel=\"noopener\">4 Contoh Confidence Interval dalam Kehidupan Nyata<\/a><br \/> <a href=\"https:\/\/statorials.org\/id\/cara-menulis-kesimpulan-selang-kepercayaan\/\" target=\"_blank\" rel=\"noopener\">Cara Menulis Kesimpulan Interval Keyakinan<\/a><br \/> 6 hipotesis interval kepercayaan untuk diperiksa<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Interval kepercayaan suatu mean adalah rentang nilai yang kemungkinan mengandung mean populasi dengan tingkat kepercayaan tertentu. Kami menggunakan rumus berikut untuk menghitung interval kepercayaan untuk suatu mean: Interval kepercayaan = x +\/- t*(s\/\u221a n ) Emas: x : mean sampel t : nilai kritis t s: deviasi standar sampel n: ukuran sampel Catatan : Kita [&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":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Cara menghitung interval kepercayaan: 3 contoh soal - Statologi<\/title>\n<meta name=\"description\" content=\"Tutorial ini memberikan beberapa contoh solusi langkah demi langkah tentang cara menghitung interval kepercayaan.\" \/>\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\/id\/contoh-soal-interval-kepercayaan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Cara menghitung interval kepercayaan: 3 contoh soal - Statologi\" \/>\n<meta property=\"og:description\" content=\"Tutorial ini memberikan beberapa contoh solusi langkah demi langkah tentang cara menghitung interval kepercayaan.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/id\/contoh-soal-interval-kepercayaan\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T13:07:19+00:00\" \/>\n<meta name=\"author\" content=\"Benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/id\/contoh-soal-interval-kepercayaan\/\",\"url\":\"https:\/\/statorials.org\/id\/contoh-soal-interval-kepercayaan\/\",\"name\":\"Cara menghitung interval kepercayaan: 3 contoh soal - Statologi\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/id\/#website\"},\"datePublished\":\"2023-07-06T13:07:19+00:00\",\"dateModified\":\"2023-07-06T13:07:19+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\"},\"description\":\"Tutorial ini memberikan beberapa contoh solusi langkah demi langkah tentang cara menghitung interval kepercayaan.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/id\/contoh-soal-interval-kepercayaan\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/id\/contoh-soal-interval-kepercayaan\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/id\/contoh-soal-interval-kepercayaan\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/statorials.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Cara menghitung interval keyakinan: 3 contoh soal\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/id\/#website\",\"url\":\"https:\/\/statorials.org\/id\/\",\"name\":\"Statorials\",\"description\":\"Panduan anda untuk kompetensi statistik!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/3d17a1160dd2d052b7c78e502cb9ec81\",\"name\":\"Benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/statorials.org\/id\/#\/schema\/person\/image\/\",\"url\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"http:\/\/statorials.org\/id\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin anderson\"},\"description\":\"Halo, saya Benjamin, pensiunan profesor statistika yang menjadi guru Statorial yang berdedikasi. 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