{"id":2015,"date":"2021-09-23T19:11:59","date_gmt":"2021-09-23T19:11:59","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2015"},"modified":"2022-02-18T05:57:04","modified_gmt":"2022-02-18T05:57:04","slug":"introduction-to-a-single-population-mean-using-the-student-t-distribution","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/introduction-to-a-single-population-mean-using-the-student-t-distribution\/","title":{"raw":"Introduction to A Single Population Mean using the Student's t-Distribution","rendered":"Introduction to A Single Population Mean using the Student&#8217;s t-Distribution"},"content":{"raw":"<h2>What you\u2019ll learn to do: construct a confidence interval for a population mean based on a t-distribution<\/h2>\r\n<img class=\"alignright wp-image-2016 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/09\/23191024\/pexels-mike-110844-300x169.jpg\" alt=\"a white electric car is being charged\" width=\"300\" height=\"169\" \/>To estimate the average distance an electric car can be driven before it needs to be recharged, researchers tested 20 cars. However, twenty is considered a small sample size and because the population standard deviation is not known, the t-distribution would be used instead of the normal distribution to create a confidence interval.","rendered":"<h2>What you\u2019ll learn to do: construct a confidence interval for a population mean based on a t-distribution<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-2016 size-medium\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5668\/2021\/09\/23191024\/pexels-mike-110844-300x169.jpg\" alt=\"a white electric car is being charged\" width=\"300\" height=\"169\" \/>To estimate the average distance an electric car can be driven before it needs to be recharged, researchers tested 20 cars. However, twenty is considered a small sample size and because the population standard deviation is not known, the t-distribution would be used instead of the normal distribution to create a confidence interval.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-2015\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li><strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>White and Orange Gasoline Nozzle. <strong>Authored by<\/strong>: Mike. <strong>Provided by<\/strong>: Pexels. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.pexels.com\/photo\/white-and-orange-gasoline-nozzle-110844\/\">https:\/\/www.pexels.com\/photo\/white-and-orange-gasoline-nozzle-110844\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169134,"menu_order":13,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"White and Orange Gasoline Nozzle\",\"author\":\"Mike\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/white-and-orange-gasoline-nozzle-110844\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2015","chapter","type-chapter","status-publish","hentry"],"part":269,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2015","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2015\/revisions"}],"predecessor-version":[{"id":3775,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2015\/revisions\/3775"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/269"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2015\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2015"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2015"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2015"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2015"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}