{"id":1180,"date":"2023-06-22T01:59:45","date_gmt":"2023-06-22T01:59:45","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-continued-learn-it-2\/"},"modified":"2025-05-16T03:13:31","modified_gmt":"2025-05-16T03:13:31","slug":"confidence-interval-for-proportions-continued-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-continued-learn-it-2\/","title":{"raw":"Confidence Interval for Proportions (continued): Learn It 2","rendered":"Confidence Interval for Proportions (continued): Learn It 2"},"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;Calculate a confidence interval and explain what it means&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;}\">Calculate a confidence interval and explain what it means.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Recognize common misinterpretations of confidence intervals&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;}\">Recognize common misinterpretations of confidence intervals.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Simulation of finding confidence intervals<\/h2>\r\n<p>Let's continue exploring the data from a national survey of college students conducted by the American College Health Association. One of the questions posed to the participants was, \u201cOn how many of the last 7 days did you take a nap?\u201d<\/p>\r\n<p>Suppose we knew that the population proportion of college students who did not take a nap in the last week was [latex]0.40[\/latex], or [latex]40\\%[\/latex]. Of course, in reality, we wouldn\u2019t know the population proportion, but let\u2019s assume that we did.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1642[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1643[\/ohm2_question]<\/section>\r\n<p>If we wanted to, we could simulate taking an even larger number of samples from this population and constructing a confidence interval for each one. Feel free to explore this further using the tool below:<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/explorecoverage\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/explorecoverage\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<p>If we were to continue to repeatedly take more and more samples from the population and construct a confidence interval for each one, we would expect the proportion of confidence intervals containing the population proportion to be equal to the chosen confidence level.<\/p>\r\n<p>Put another way, if we were constructing [latex]95\\%[\/latex] confidence intervals, then in the long run, we would expect [latex]95\\%[\/latex] of the intervals to contain the population proportion.<\/p>\r\n<p>An important takeaway is that the chosen confidence level is associated with the method used to create the interval and not the likelihood that an individual interval contains the population proportion.<\/p>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate a confidence interval and explain what it means&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;}\">Calculate a confidence interval and explain what it means.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Recognize common misinterpretations of confidence intervals&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;}\">Recognize common misinterpretations of confidence intervals.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Simulation of finding confidence intervals<\/h2>\n<p>Let&#8217;s continue exploring the data from a national survey of college students conducted by the American College Health Association. One of the questions posed to the participants was, \u201cOn how many of the last 7 days did you take a nap?\u201d<\/p>\n<p>Suppose we knew that the population proportion of college students who did not take a nap in the last week was [latex]0.40[\/latex], or [latex]40\\%[\/latex]. Of course, in reality, we wouldn\u2019t know the population proportion, but let\u2019s assume that we did.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1642\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1642&theme=lumen&iframe_resize_id=ohm1642&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1643\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1643&theme=lumen&iframe_resize_id=ohm1643&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>If we wanted to, we could simulate taking an even larger number of samples from this population and constructing a confidence interval for each one. Feel free to explore this further using the tool below:<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/explorecoverage\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/explorecoverage\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<p>If we were to continue to repeatedly take more and more samples from the population and construct a confidence interval for each one, we would expect the proportion of confidence intervals containing the population proportion to be equal to the chosen confidence level.<\/p>\n<p>Put another way, if we were constructing [latex]95\\%[\/latex] confidence intervals, then in the long run, we would expect [latex]95\\%[\/latex] of the intervals to contain the population proportion.<\/p>\n<p>An important takeaway is that the chosen confidence level is associated with the method used to create the interval and not the likelihood that an individual interval contains the population proportion.<\/p>\n","protected":false},"author":8,"menu_order":17,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1163,"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\/1180"}],"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":6,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1180\/revisions"}],"predecessor-version":[{"id":6730,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1180\/revisions\/6730"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1163"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1180\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1180"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1180"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1180"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1180"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}