{"id":1517,"date":"2023-06-22T02:40:16","date_gmt":"2023-06-22T02:40:16","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/bootstrap-confidence-interval-learn-it-1\/"},"modified":"2025-05-17T02:52:36","modified_gmt":"2025-05-17T02:52:36","slug":"bootstrap-confidence-interval-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/bootstrap-confidence-interval-learn-it-1\/","title":{"raw":"Bootstrap Confidence Interval - Learn it 1","rendered":"Bootstrap Confidence Interval &#8211; Learn it 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find a bootstrap confidence interval for a population parameter and difference in population parameters&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Find a bootstrap confidence interval for a population parameter and difference in population parameters<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Describe what a bootstrap confidence interval means and use it make inference regarding the population&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Describe what a bootstrap confidence interval means and use it make inference regarding the population<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Bootstrap Confidence Interval for a Population Parameter<\/h2>\r\n<p>Previously, a bootstrap confidence interval for a population mean was constructed by using percentiles from a bootstrap distribution formed by calculating the value of the sample mean for a large number of bootstrap samples. But, what if we wanted to get a confidence interval for a different population parameter?<\/p>\r\n<p>For example, maybe a population distribution is quite skewed, so the <strong>median<\/strong> might be a better choice for describing the center of the distribution. Could we use sample data to calculate a confidence interval for the population median? There is no [latex]t[\/latex] confidence interval or [latex]z[\/latex] confidence interval for a population median.<\/p>\r\n<p>In the previous in-class activity, we were able to use sample data to construct a bootstrap confidence interval for a population mean by carrying out the following steps:<\/p>\r\n<ol>\r\n\t<li>Create a bootstrap sample by selecting a sample with replacement from the original sample.<\/li>\r\n\t<li>Calculate the sample mean for the bootstrap sample.<\/li>\r\n\t<li>Repeat Steps [latex]1[\/latex] and [latex]2[\/latex] a large number of times.<\/li>\r\n\t<li>Create a bootstrap distribution of the bootstrap sample means and then determine the end points of the confidence interval by using appropriate percentiles of the bootstrap distribution.<\/li>\r\n<\/ol>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3115[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Find a bootstrap confidence interval for a population parameter and difference in population parameters&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Find a bootstrap confidence interval for a population parameter and difference in population parameters<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Describe what a bootstrap confidence interval means and use it make inference regarding the population&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Describe what a bootstrap confidence interval means and use it make inference regarding the population<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Bootstrap Confidence Interval for a Population Parameter<\/h2>\n<p>Previously, a bootstrap confidence interval for a population mean was constructed by using percentiles from a bootstrap distribution formed by calculating the value of the sample mean for a large number of bootstrap samples. But, what if we wanted to get a confidence interval for a different population parameter?<\/p>\n<p>For example, maybe a population distribution is quite skewed, so the <strong>median<\/strong> might be a better choice for describing the center of the distribution. Could we use sample data to calculate a confidence interval for the population median? There is no [latex]t[\/latex] confidence interval or [latex]z[\/latex] confidence interval for a population median.<\/p>\n<p>In the previous in-class activity, we were able to use sample data to construct a bootstrap confidence interval for a population mean by carrying out the following steps:<\/p>\n<ol>\n<li>Create a bootstrap sample by selecting a sample with replacement from the original sample.<\/li>\n<li>Calculate the sample mean for the bootstrap sample.<\/li>\n<li>Repeat Steps [latex]1[\/latex] and [latex]2[\/latex] a large number of times.<\/li>\n<li>Create a bootstrap distribution of the bootstrap sample means and then determine the end points of the confidence interval by using appropriate percentiles of the bootstrap distribution.<\/li>\n<\/ol>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3115\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3115&theme=lumen&iframe_resize_id=ohm3115&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":14,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1502,"module-header":"learn_it","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1517"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":5,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1517\/revisions"}],"predecessor-version":[{"id":6926,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1517\/revisions\/6926"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1502"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1517\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1517"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1517"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1517"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1517"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}