{"id":1546,"date":"2013-01-08T00:06:42","date_gmt":"2013-01-07T15:06:42","guid":{"rendered":"http:\/\/fujiitoshiki.com\/improvesociety\/?p=1546"},"modified":"2014-08-08T05:55:48","modified_gmt":"2014-08-07T20:55:48","slug":"how-to-estimate-95-confidence-interval-of-population-average-from-sample-average-and-sample-standard-deviation","status":"publish","type":"post","link":"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=1546","title":{"rendered":"How to estimate 95 % confidence interval of population average from sample average and sample standard deviation?"},"content":{"rendered":"<div class=\"theContentWrap-ccc\"><p>If you had known average and standard deviation of sample which size is N, you could estimate the range of population average with 95 % probability. In standard normal distribution, sum of area under curve greater than 1.96 and less than &#8211; 1.96 is 0.05. There is population average between exception multiplying 1.96 by standard error from average and sum of the multiplied and average, called as 95 % confidence interval (95 % CI).<\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cdisplaystyle+95+%5C%25+C.I.%3D+%5Cmu+%5Cpm+1.96+SE+%3D+%5Cmu+%5Cpm+1.96+%5Cfrac%7BSD%7D%7B%5Csqrt+N%7D&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\displaystyle 95 \\% C.I.= \\mu \\pm 1.96 SE = \\mu \\pm 1.96 \\frac{SD}{\\sqrt N}' title='\\displaystyle 95 \\% C.I.= \\mu \\pm 1.96 SE = \\mu \\pm 1.96 \\frac{SD}{\\sqrt N}' class='latex' \/><\/p>\n<p><img src='https:\/\/s0.wp.com\/latex.php?latex=%5Cmu&#038;bg=T&#038;fg=000000&#038;s=0' alt='\\mu' title='\\mu' class='latex' \/>; Average, SE; standard error, SD; standard deviation<\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>If you had known average and standard deviation of sample which size is N, you could estimate the range of pop &hellip; <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=1546\" class=\"more-link\"><span class=\"screen-reader-text\">&#8220;How to estimate 95 % confidence interval of population average from sample average and sample standard deviation?&#8221; \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[7],"tags":[42,46,47,48],"class_list":["post-1546","post","type-post","status-publish","format-standard","hentry","category-statistics","tag-95-confidence-interval","tag-population-average","tag-sample-average","tag-sample-standard-deviation"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/1546","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1546"}],"version-history":[{"count":8,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/1546\/revisions"}],"predecessor-version":[{"id":6175,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/1546\/revisions\/6175"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1546"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1546"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}