{"id":1181,"date":"2023-06-22T01:59:46","date_gmt":"2023-06-22T01:59:46","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-continued-learn-it-3\/"},"modified":"2025-05-16T03:13:44","modified_gmt":"2025-05-16T03:13:44","slug":"confidence-interval-for-proportions-continued-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-continued-learn-it-3\/","title":{"raw":"Confidence Interval for Proportions (continued): Learn It 3","rendered":"Confidence Interval for Proportions (continued): Learn It 3"},"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>Interpretation of a confidence interval<\/h2>\r\n<p>As we simulated finding confidence intervals, we learned that a chosen level of confidence is associated with the method used to create the interval and not the likelihood that an individual interval contains the population proportion.<\/p>\r\n<p class=\"studentredanswer\" style=\"margin-left: 0in;\"><span style=\"color: windowtext;\">This means that any time we provide a statement to interpret a confidence interval's meaning, we should state that the <b>confidence level is a measure of our confidence in the method.<\/b><\/span><\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1040[\/ohm2_question]<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/inference_prop\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/inference_prop\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1041[\/ohm2_question]<\/section>\r\n<section class=\"textbox proTip\">The interpretation of a confidence interval depends on the confidence level. For example, using a [latex]95\\%[\/latex] confidence level, the interpretation would be:<strong><br \/>\r\nWe can be [latex]95\\%[\/latex] confident that the interval from ___ to ___ captures the true population proportion of _______.<\/strong><\/section>","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>Interpretation of a confidence interval<\/h2>\n<p>As we simulated finding confidence intervals, we learned that a chosen level of confidence is associated with the method used to create the interval and not the likelihood that an individual interval contains the population proportion.<\/p>\n<p class=\"studentredanswer\" style=\"margin-left: 0in;\"><span style=\"color: windowtext;\">This means that any time we provide a statement to interpret a confidence interval&#8217;s meaning, we should state that the <b>confidence level is a measure of our confidence in the method.<\/b><\/span><\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1040\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1040&theme=lumen&iframe_resize_id=ohm1040&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/inference_prop\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/inference_prop\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1041\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1041&theme=lumen&iframe_resize_id=ohm1041&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox proTip\">The interpretation of a confidence interval depends on the confidence level. For example, using a [latex]95\\%[\/latex] confidence level, the interpretation would be:<strong><br \/>\nWe can be [latex]95\\%[\/latex] confident that the interval from ___ to ___ captures the true population proportion of _______.<\/strong><\/section>\n","protected":false},"author":8,"menu_order":18,"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\/1181"}],"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":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1181\/revisions"}],"predecessor-version":[{"id":6731,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1181\/revisions\/6731"}],"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\/1181\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1181"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1181"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1181"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1181"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}