{"id":4911,"date":"2023-07-06T13:07:19","date_gmt":"2023-07-06T13:07:19","guid":{"rendered":"https:\/\/statorials.org\/pt\/problemas-de-exemplo-de-intervalo-de-confianca\/"},"modified":"2023-07-06T13:07:19","modified_gmt":"2023-07-06T13:07:19","slug":"problemas-de-exemplo-de-intervalo-de-confianca","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/problemas-de-exemplo-de-intervalo-de-confianca\/","title":{"rendered":"Como calcular intervalos de confian\u00e7a: 3 exemplos de problemas"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Um <strong>intervalo de confian\u00e7a para uma m\u00e9dia<\/strong> \u00e9 um intervalo de valores que provavelmente cont\u00e9m uma <a href=\"https:\/\/statorials.org\/pt\/media-amostral-em-comparacao-com-a-media-populacional\/\" target=\"_blank\" rel=\"noopener\">m\u00e9dia populacional<\/a> com um certo n\u00edvel de confian\u00e7a.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Usamos a seguinte f\u00f3rmula para calcular um intervalo de confian\u00e7a para uma m\u00e9dia:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a =<\/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;\">Ouro:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> :<\/strong> m\u00e9dias amostrais<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>t:<\/strong> o valor cr\u00edtico de t<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> desvio padr\u00e3o da amostra<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> tamanho da amostra<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>Nota<\/strong> : Substitu\u00edmos o valor cr\u00edtico por um valor cr\u00edtico z na f\u00f3rmula se o desvio padr\u00e3o da popula\u00e7\u00e3o (\u03c3) for conhecido <em>e<\/em> o tamanho da amostra for maior que 30.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Os exemplos a seguir mostram como construir um intervalo de confian\u00e7a para uma m\u00e9dia em tr\u00eas cen\u00e1rios diferentes:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">O desvio padr\u00e3o populacional (\u03c3) \u00e9 desconhecido<\/span><\/li>\n<li> <span style=\"color: #000000;\">O desvio padr\u00e3o populacional (\u03c3) \u00e9 conhecido, mas n \u2264 30<\/span><\/li>\n<li> <span style=\"color: #000000;\">O desvio padr\u00e3o populacional (\u03c3) \u00e9 conhecido en &gt; 30<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Vamos!<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Exemplo 1: intervalo de confian\u00e7a quando \u03c3 \u00e9 desconhecido<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Suponha que queiramos calcular um intervalo de confian\u00e7a de 95% para a altura m\u00e9dia (em polegadas) de uma determinada esp\u00e9cie de planta.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Suponha que coletamos uma amostra aleat\u00f3ria simples com as seguintes informa\u00e7\u00f5es:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">m\u00e9dia amostral ( <span style=\"text-decoration: overline;\">x<\/span> ) = 12<\/span><\/li>\n<li> <span style=\"color: #000000;\">tamanho da amostra (n) = 19<\/span><\/li>\n<li> <span style=\"color: #000000;\">desvio padr\u00e3o(s) amostral(s) = 6,3<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Podemos usar a seguinte f\u00f3rmula para construir esse intervalo de confian\u00e7a:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">IC 95% = <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;\">IC 95% = 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;\">IC 95% = 12 +\/- t <sub>18,025<\/sub> *(6,3\/\u221a <span style=\"text-decoration: overline;\">19<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">IC 95% = 12 +\/- 2,1009*(6,3\/\u221a <span style=\"text-decoration: overline;\">19<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">IC 95% = <strong>(8.964, 15.037)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O intervalo de confian\u00e7a de 95% para a altura m\u00e9dia da popula\u00e7\u00e3o para esta esp\u00e9cie de planta espec\u00edfica \u00e9 <strong>(8,964 polegadas, 15,037 polegadas)<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Nota n\u00ba 1<\/strong> : Usamos a calculadora de distribui\u00e7\u00e3o t inversa para encontrar o valor t cr\u00edtico associado a 18 graus de liberdade e um n\u00edvel de confian\u00e7a de 0,95.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Nota #2<\/strong> : Como o desvio padr\u00e3o populacional (\u03c3) \u00e9 desconhecido, utilizamos o valor cr\u00edtico t no c\u00e1lculo do intervalo de confian\u00e7a.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Exemplo 2:<\/strong><\/span> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a quando \u03c3 \u00e9 conhecido, mas n \u2264 30<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Suponha que queiramos calcular um intervalo de confian\u00e7a de 99% para a nota m\u00e9dia de um determinado vestibular.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Suponha que coletamos uma amostra aleat\u00f3ria simples com as seguintes informa\u00e7\u00f5es:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">m\u00e9dia amostral ( <span style=\"text-decoration: overline;\">x<\/span> ) = 85<\/span><\/li>\n<li> <span style=\"color: #000000;\">tamanho da amostra (n) = 25<\/span><\/li>\n<li> <span style=\"color: #000000;\">desvio padr\u00e3o populacional (\u03c3) = 3,5<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Podemos usar a seguinte f\u00f3rmula para construir esse intervalo de confian\u00e7a:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">IC 99% = <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;\">IC 99% = 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;\">IC 99% = 85 +\/- t <sub>24,005<\/sub> *(3,5\/\u221a <span style=\"text-decoration: overline;\">25<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">IC 99% = 85 +\/- 2,7969*(3,5\/\u221a <span style=\"text-decoration: overline;\">25<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">IC 99% = <strong>(83,042, 86,958)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O intervalo de confian\u00e7a de 99% para a nota m\u00e9dia da popula\u00e7\u00e3o neste vestibular \u00e9 <strong>(83,042, 86,958)<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Nota n\u00ba 1<\/strong> : Usamos a calculadora de distribui\u00e7\u00e3o t inversa para encontrar o valor t cr\u00edtico associado a 24 graus de liberdade e um n\u00edvel de confian\u00e7a de 0,99.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Nota #2<\/strong> : Como o desvio padr\u00e3o populacional (\u03c3) era conhecido, mas o tamanho da amostra (n) era inferior a 30, utilizamos o valor cr\u00edtico t no c\u00e1lculo do intervalo de confian\u00e7a.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Exemplo 3:<\/strong><\/span> <span style=\"color: #000000;\"><strong>Intervalo de confian\u00e7a quando \u03c3 \u00e9 conhecido en &gt; 30<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Suponha que queiramos calcular um intervalo de confian\u00e7a de 90% para o peso m\u00e9dio de uma determinada esp\u00e9cie de tartaruga.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Suponha que coletamos uma amostra aleat\u00f3ria simples com as seguintes informa\u00e7\u00f5es:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">m\u00e9dia amostral ( <span style=\"text-decoration: overline;\">x<\/span> ) = 300<\/span><\/li>\n<li> <span style=\"color: #000000;\">tamanho da amostra (n) = 40<\/span><\/li>\n<li> <span style=\"color: #000000;\">desvio padr\u00e3o populacional (\u03c3) = 15<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Podemos usar a seguinte f\u00f3rmula para construir esse intervalo de confian\u00e7a:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">IC 90% = <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;\">IC 90% = 300 +\/- 1,645*(15\/\u221a <span style=\"text-decoration: overline;\">40<\/span> )<\/span><\/li>\n<li> <span style=\"color: #000000;\">IC 90% = <strong>(296.099, 303.901)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">O intervalo de confian\u00e7a de 90% para o peso m\u00e9dio da popula\u00e7\u00e3o desta esp\u00e9cie de tartaruga em particular \u00e9 <strong>(83,042, 86,958)<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Nota n\u00ba 1<\/strong> : Usamos a Calculadora do Valor Z Cr\u00edtico para encontrar o valor z cr\u00edtico associado a um n\u00edvel de signific\u00e2ncia de 0,1.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Nota #2<\/strong> : Como o desvio padr\u00e3o populacional (\u03c3) era conhecido e o tamanho da amostra (n) era maior que 30, utilizamos o valor cr\u00edtico z no c\u00e1lculo do intervalo de confian\u00e7a.<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Recursos adicionais<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">Os tutoriais a seguir fornecem informa\u00e7\u00f5es adicionais sobre intervalos de confian\u00e7a:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/pt\/exemplo-real-de-intervalo-de-confianca\/\" target=\"_blank\" rel=\"noopener\">4 exemplos de intervalos de confian\u00e7a na vida real<\/a><br \/> <a href=\"https:\/\/statorials.org\/pt\/como-escrever-a-conclusao-do-intervalo-de-confianca\/\" target=\"_blank\" rel=\"noopener\">Como escrever uma conclus\u00e3o sobre intervalo de confian\u00e7a<\/a><br \/> As 6 hip\u00f3teses de intervalo de confian\u00e7a a serem verificadas<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Um intervalo de confian\u00e7a para uma m\u00e9dia \u00e9 um intervalo de valores que provavelmente cont\u00e9m uma m\u00e9dia populacional com um certo n\u00edvel de confian\u00e7a. Usamos a seguinte f\u00f3rmula para calcular um intervalo de confian\u00e7a para uma m\u00e9dia: Intervalo de confian\u00e7a = x +\/- t*(s\/\u221a n ) Ouro: x : m\u00e9dias amostrais t: o valor cr\u00edtico [&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-4911","post","type-post","status-publish","format-standard","hentry","category-guia"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Como calcular intervalos de confian\u00e7a: 3 exemplos de problemas - Estatologia<\/title>\n<meta name=\"description\" content=\"Este tutorial fornece v\u00e1rios exemplos com solu\u00e7\u00f5es passo a passo sobre como calcular intervalos de confian\u00e7a.\" \/>\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\/pt\/problemas-de-exemplo-de-intervalo-de-confianca\/\" \/>\n<meta property=\"og:locale\" content=\"pt_PT\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Como calcular intervalos de confian\u00e7a: 3 exemplos de problemas - Estatologia\" \/>\n<meta property=\"og:description\" content=\"Este tutorial fornece v\u00e1rios exemplos com solu\u00e7\u00f5es passo a passo sobre como calcular intervalos de confian\u00e7a.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pt\/problemas-de-exemplo-de-intervalo-de-confianca\/\" \/>\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=\"Dr. benjamim anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Escrito por\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. benjamim anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tempo estimado de leitura\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutos\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pt\/problemas-de-exemplo-de-intervalo-de-confianca\/\",\"url\":\"https:\/\/statorials.org\/pt\/problemas-de-exemplo-de-intervalo-de-confianca\/\",\"name\":\"Como calcular intervalos de confian\u00e7a: 3 exemplos de problemas - Estatologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pt\/#website\"},\"datePublished\":\"2023-07-06T13:07:19+00:00\",\"dateModified\":\"2023-07-06T13:07:19+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\"},\"description\":\"Este tutorial fornece v\u00e1rios exemplos com solu\u00e7\u00f5es passo a passo sobre como calcular intervalos de confian\u00e7a.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pt\/problemas-de-exemplo-de-intervalo-de-confianca\/#breadcrumb\"},\"inLanguage\":\"pt-PT\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pt\/problemas-de-exemplo-de-intervalo-de-confianca\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pt\/problemas-de-exemplo-de-intervalo-de-confianca\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Lar\",\"item\":\"https:\/\/statorials.org\/pt\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Como calcular intervalos de confian\u00e7a: 3 exemplos de problemas\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pt\/#website\",\"url\":\"https:\/\/statorials.org\/pt\/\",\"name\":\"Statorials\",\"description\":\"O seu guia para a literacia estat\u00edstica!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pt\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pt-PT\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/e08f98e8db95e0aa9c310e1b27c9c666\",\"name\":\"Dr. benjamim anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pt-PT\",\"@id\":\"https:\/\/statorials.org\/pt\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pt\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr. benjamim anderson\"},\"description\":\"Ol\u00e1, sou Benjamin, um professor aposentado de estat\u00edstica que se tornou professor dedicado na Statorials. 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