{"id":1196,"date":"2023-06-22T01:59:57","date_gmt":"2023-06-22T01:59:57","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-intervals-for-the-difference-in-population-proportions-learn-it-3\/"},"modified":"2025-05-16T03:18:43","modified_gmt":"2025-05-16T03:18:43","slug":"confidence-intervals-for-the-difference-in-population-proportions-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-intervals-for-the-difference-in-population-proportions-learn-it-3\/","title":{"raw":"Confidence Intervals for the Difference in Population Proportions: Learn It 4","rendered":"Confidence Intervals for the Difference in Population Proportions: Learn It 4"},"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>Confidence interval for the difference in proportions<\/h2>\r\n<p>To estimate a difference between two population proportions (or the size of a treatment effect), we select <strong>two independent random samples<\/strong> and use the difference in sample proportions as an estimate. Of course, random samples vary, so we want to include a statement about the amount of error that may be present. Because the differences in sample proportions vary in a predictable way, we can also make a probability statement about how confident we are in the process that we used to estimate the difference between the population proportions. This describes a confidence interval.<\/p>\r\n<p>Let's focus on using technology to calculate the confidence interval for the difference between two population proportions for independent groups.<\/p>\r\n<section class=\"textbox interact\">Steps to calculate the confidence interval:\r\n\r\n<p style=\"padding-left: 40px;\"><strong>Step 1: <\/strong>To enter the summary data at the beginning of this preview assignment, select <strong>Number of Successes<\/strong> under <strong>Enter Data<\/strong>\u00a0on the left-hand side.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 2: <\/strong>Since we are interested in calculating the confidence interval for [latex] \\hat{p}_{group1} - \\hat{p}_{group2}[\/latex], assign the correct variable to Group 1 and Group 2.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 3: <\/strong>Enter the number of successes and sample sizes for each group in the tool. You can add informative group labels by clicking <strong>Provide Labels for: Groups<\/strong>.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 4: <\/strong>Change the confidence interval using the slider on the left-hand side accordingly.<\/p>\r\n<\/section>\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]1688[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1045[\/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>Confidence interval for the difference in proportions<\/h2>\n<p>To estimate a difference between two population proportions (or the size of a treatment effect), we select <strong>two independent random samples<\/strong> and use the difference in sample proportions as an estimate. Of course, random samples vary, so we want to include a statement about the amount of error that may be present. Because the differences in sample proportions vary in a predictable way, we can also make a probability statement about how confident we are in the process that we used to estimate the difference between the population proportions. This describes a confidence interval.<\/p>\n<p>Let&#8217;s focus on using technology to calculate the confidence interval for the difference between two population proportions for independent groups.<\/p>\n<section class=\"textbox interact\">Steps to calculate the confidence interval:<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 1: <\/strong>To enter the summary data at the beginning of this preview assignment, select <strong>Number of Successes<\/strong> under <strong>Enter Data<\/strong>\u00a0on the left-hand side.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 2: <\/strong>Since we are interested in calculating the confidence interval for [latex]\\hat{p}_{group1} - \\hat{p}_{group2}[\/latex], assign the correct variable to Group 1 and Group 2.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 3: <\/strong>Enter the number of successes and sample sizes for each group in the tool. You can add informative group labels by clicking <strong>Provide Labels for: Groups<\/strong>.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 4: <\/strong>Change the confidence interval using the slider on the left-hand side accordingly.<\/p>\n<\/section>\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=\"ohm1688\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1688&theme=lumen&iframe_resize_id=ohm1688&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1045\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1045&theme=lumen&iframe_resize_id=ohm1045&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":31,"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\/1196"}],"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":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1196\/revisions"}],"predecessor-version":[{"id":6741,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1196\/revisions\/6741"}],"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\/1196\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1196"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1196"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1196"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1196"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}