{"id":1201,"date":"2023-06-22T02:00:03","date_gmt":"2023-06-22T02:00:03","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-intervals-for-the-difference-in-population-proportions-apply-it-5\/"},"modified":"2025-05-16T03:20:12","modified_gmt":"2025-05-16T03:20:12","slug":"confidence-intervals-for-the-difference-in-population-proportions-apply-it-5","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-intervals-for-the-difference-in-population-proportions-apply-it-5\/","title":{"raw":"Confidence Intervals for the Difference in Population Proportions: Apply It 3","rendered":"Confidence Intervals for the Difference in Population Proportions: Apply 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 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>Conditions for the Confidence Intervals for the Difference in Proportions<\/h2>\r\n<p>Similar to when we use a confidence interval to draw conclusions about a single proportion, we need to check a set of conditions to ensure the interval is appropriate for the data.<\/p>\r\n<section class=\"textbox recall\">The three conditions when calculating confidence intervals for the difference between two proportions are:\r\n\r\n<ul>\r\n\t<li>Random samples: The observations represent a random sample of the population.<\/li>\r\n\t<li>Independence: The samples are independently selected.<\/li>\r\n\t<li>Sample size: [latex] n_{1}\\hat{p}_{1} \\geq 10 [\/latex] and [latex] n_{2}\\hat{p}_{2} \\geq 10 [\/latex]<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]922[\/ohm2_question]<\/section>\r\n<h3>Making Inferences<\/h3>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]923[\/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>Conditions for the Confidence Intervals for the Difference in Proportions<\/h2>\n<p>Similar to when we use a confidence interval to draw conclusions about a single proportion, we need to check a set of conditions to ensure the interval is appropriate for the data.<\/p>\n<section class=\"textbox recall\">The three conditions when calculating confidence intervals for the difference between two proportions are:<\/p>\n<ul>\n<li>Random samples: The observations represent a random sample of the population.<\/li>\n<li>Independence: The samples are independently selected.<\/li>\n<li>Sample size: [latex]n_{1}\\hat{p}_{1} \\geq 10[\/latex] and [latex]n_{2}\\hat{p}_{2} \\geq 10[\/latex]<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm922\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=922&theme=lumen&iframe_resize_id=ohm922&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h3>Making Inferences<\/h3>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm923\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=923&theme=lumen&iframe_resize_id=ohm923&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":34,"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":"apply_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\/1201"}],"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":9,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1201\/revisions"}],"predecessor-version":[{"id":6744,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1201\/revisions\/6744"}],"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\/1201\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1201"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1201"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1201"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1201"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}