{"id":1202,"date":"2023-06-22T02:00:04","date_gmt":"2023-06-22T02:00:04","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-intervals-for-the-difference-in-population-proportions-dig-deeper\/"},"modified":"2025-05-16T03:20:43","modified_gmt":"2025-05-16T03:20:43","slug":"confidence-intervals-for-the-difference-in-population-proportions-dig-deeper","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-intervals-for-the-difference-in-population-proportions-dig-deeper\/","title":{"raw":"Confidence Intervals for the Difference in Population Proportions: Fresh Take","rendered":"Confidence Intervals for the Difference in Population Proportions: Fresh Take"},"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 for the difference in proportions of two groups&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 for the difference in proportions of two groups.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Make conclusions based on a confidence interval&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;}\">Make conclusions based on a confidence interval.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Is Yawning Contagious?<\/h2>\r\n<p>The objective of this analysis is to explore the proportion of people who yawn after seeing someone else yawn. We will use data[footnote] from the yawn data set in the OpenIntro R package. https:\/\/www.openintro.org\/data\/index.php?data=yawn[\/footnote] from an experiment conducted on the television show Mythbusters.<\/p>\r\n<p>In the experiment, 50 participants were randomly assigned to two groups:<\/p>\r\n<ul>\r\n\t<li>Treatment (34 participants), who saw a person near them yawn<\/li>\r\n\t<li>Control (16 participants), who didn\u2019t see anyone yawn<\/li>\r\n<\/ul>\r\n<p>All of the participants were instructed to wait in a room, and the experimenters recorded whether or not the participants yawned. The participants arrived at different times, so no two participants were in the waiting room at the same time.<\/p>\r\n<p>For the 34 participants in the treatment group, 10 participants yawned and 24 participants didn't.<\/p>\r\n<p>For the 16 participants in the control group, 4 participants yawned and 12 participants didn't.<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/2sample_prop\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/2sample_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]2805[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2806[\/ohm2_question]<\/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 for the difference in proportions of two groups&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 for the difference in proportions of two groups.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Make conclusions based on a confidence interval&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;}\">Make conclusions based on a confidence interval.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Is Yawning Contagious?<\/h2>\n<p>The objective of this analysis is to explore the proportion of people who yawn after seeing someone else yawn. We will use data<a class=\"footnote\" title=\"from the yawn data set in the OpenIntro R package. https:\/\/www.openintro.org\/data\/index.php?data=yawn\" id=\"return-footnote-1202-1\" href=\"#footnote-1202-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> from an experiment conducted on the television show Mythbusters.<\/p>\n<p>In the experiment, 50 participants were randomly assigned to two groups:<\/p>\n<ul>\n<li>Treatment (34 participants), who saw a person near them yawn<\/li>\n<li>Control (16 participants), who didn\u2019t see anyone yawn<\/li>\n<\/ul>\n<p>All of the participants were instructed to wait in a room, and the experimenters recorded whether or not the participants yawned. The participants arrived at different times, so no two participants were in the waiting room at the same time.<\/p>\n<p>For the 34 participants in the treatment group, 10 participants yawned and 24 participants didn&#8217;t.<\/p>\n<p>For the 16 participants in the control group, 4 participants yawned and 12 participants didn&#8217;t.<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/2sample_prop\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/2sample_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=\"ohm2805\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2805&theme=lumen&iframe_resize_id=ohm2805&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2806\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2806&theme=lumen&iframe_resize_id=ohm2806&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1202-1\"> from the yawn data set in the OpenIntro R package. https:\/\/www.openintro.org\/data\/index.php?data=yawn <a href=\"#return-footnote-1202-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":35,"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":"fresh_take","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\/1202"}],"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\/1202\/revisions"}],"predecessor-version":[{"id":6745,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1202\/revisions\/6745"}],"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\/1202\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1202"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1202"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1202"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1202"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}