{"id":1197,"date":"2023-06-22T01:59:58","date_gmt":"2023-06-22T01:59:58","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-intervals-for-the-difference-in-population-proportions-apply-it-1\/"},"modified":"2025-05-16T03:19:25","modified_gmt":"2025-05-16T03:19:25","slug":"confidence-intervals-for-the-difference-in-population-proportions-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-intervals-for-the-difference-in-population-proportions-apply-it-1\/","title":{"raw":"Confidence Intervals for the Difference in Population Proportions: Apply It 1","rendered":"Confidence Intervals for the Difference in Population Proportions: Apply It 1"},"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>Analyzing voting behavior<\/h2>\r\n<p><img class=\"aligncenter wp-image-127 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211553\/Picture1-3.jpg\" alt=\"Image of a person voting at a voting booth.\" width=\"300\" height=\"201\" \/><\/p>\r\n<p>One of the most important rights of American citizens is the franchise\u2014the right to vote.[footnote]https:\/\/www.whitehouse.gov\/about-the-white-house\/our-government\/elections-and-voting\/[\/footnote] The American electoral system is called a two-party system. That means that two parties dominate the political field. They are the Republican Party and the Democratic Party.[footnote]https:\/\/en.wikipedia.org\/wiki\/Political_parties_in_the_United_States[\/footnote]<\/p>\r\n<p>Let's investigate if there are differences in voting behaviors between eligible voters who affiliate with one of the two major political parties in the United States (Democrats and Republicans) and those who do not. Specifically, we will look at the difference in the proportions of \u201cregular voters\u201d between the two groups. In these data, a \u201cregular voter\u201d is a person who indicated that they voted in \u201call or all-but-one of the elections they were eligible for\u201d in the survey.<\/p>\r\n<p>The authors in the <em>FiveThirtyEight<\/em> article \u201cWhy Many Americans Don\u2019t Vote\u201d[footnote]Thomson-DeVeaux, A., Mithani, J., &amp; Bronner, L. (2020, October 26). Why many Americans don\u2019t vote. FiveThirtyEight. https:\/\/projects.fivethirtyeight.com\/non-voters-poll-2020-election\/[\/footnote] limited their analysis to only include survey responses from voters who were eligible for at least four election cycles. For this activity, we will also limit our data to this group.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]921[\/ohm2_question]<\/section>\r\n<p>The data come from the data journalism website <a href=\"https:\/\/projects.fivethirtyeight.com\/non-voters-poll-2020-election\/\"><em>FiveThirtyEight<\/em>.<\/a> The data were originally collected as part of an online survey conducted by Ipsos, where respondents answered demographic questions along with questions about political party affiliation and voting behavior.<\/p>\r\n<p>The data contain information for [latex]3,594[\/latex] respondents who said they identify with a major party (Republican or Democrat) and [latex]2,242[\/latex] respondents who said they do not have a major party affiliation. All the respondents had been eligible to vote for at least four election cycles at the time of the survey. The primary variables of interest are:<\/p>\r\n<ul>\r\n\t<li><em>party_id<\/em>: Republican, Democrat, or Other<\/li>\r\n\t<li><em>major_party<\/em>: Yes if the respondent identified as Republican or Democrat; no otherwise<\/li>\r\n\t<li><em>regular_voter<\/em>: Yes if the respondent voted in all or all-but-one of the elections they were eligible for; no otherwise<\/li>\r\n<\/ul>\r\n<p>Of the [latex]3,594[\/latex] respondents with a major party affiliation, [latex]1,255[\/latex] were regular voters. Of the [latex]2,242[\/latex] respondents with no major party affiliation, [latex]556[\/latex] were regular voters.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1681[\/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>Analyzing voting behavior<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-127 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211553\/Picture1-3.jpg\" alt=\"Image of a person voting at a voting booth.\" width=\"300\" height=\"201\" \/><\/p>\n<p>One of the most important rights of American citizens is the franchise\u2014the right to vote.<a class=\"footnote\" title=\"https:\/\/www.whitehouse.gov\/about-the-white-house\/our-government\/elections-and-voting\/\" id=\"return-footnote-1197-1\" href=\"#footnote-1197-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> The American electoral system is called a two-party system. That means that two parties dominate the political field. They are the Republican Party and the Democratic Party.<a class=\"footnote\" title=\"https:\/\/en.wikipedia.org\/wiki\/Political_parties_in_the_United_States\" id=\"return-footnote-1197-2\" href=\"#footnote-1197-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<p>Let&#8217;s investigate if there are differences in voting behaviors between eligible voters who affiliate with one of the two major political parties in the United States (Democrats and Republicans) and those who do not. Specifically, we will look at the difference in the proportions of \u201cregular voters\u201d between the two groups. In these data, a \u201cregular voter\u201d is a person who indicated that they voted in \u201call or all-but-one of the elections they were eligible for\u201d in the survey.<\/p>\n<p>The authors in the <em>FiveThirtyEight<\/em> article \u201cWhy Many Americans Don\u2019t Vote\u201d<a class=\"footnote\" title=\"Thomson-DeVeaux, A., Mithani, J., &amp; Bronner, L. (2020, October 26). Why many Americans don\u2019t vote. FiveThirtyEight. https:\/\/projects.fivethirtyeight.com\/non-voters-poll-2020-election\/\" id=\"return-footnote-1197-3\" href=\"#footnote-1197-3\" aria-label=\"Footnote 3\"><sup class=\"footnote\">[3]<\/sup><\/a> limited their analysis to only include survey responses from voters who were eligible for at least four election cycles. For this activity, we will also limit our data to this group.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm921\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=921&theme=lumen&iframe_resize_id=ohm921&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>The data come from the data journalism website <a href=\"https:\/\/projects.fivethirtyeight.com\/non-voters-poll-2020-election\/\"><em>FiveThirtyEight<\/em>.<\/a> The data were originally collected as part of an online survey conducted by Ipsos, where respondents answered demographic questions along with questions about political party affiliation and voting behavior.<\/p>\n<p>The data contain information for [latex]3,594[\/latex] respondents who said they identify with a major party (Republican or Democrat) and [latex]2,242[\/latex] respondents who said they do not have a major party affiliation. All the respondents had been eligible to vote for at least four election cycles at the time of the survey. The primary variables of interest are:<\/p>\n<ul>\n<li><em>party_id<\/em>: Republican, Democrat, or Other<\/li>\n<li><em>major_party<\/em>: Yes if the respondent identified as Republican or Democrat; no otherwise<\/li>\n<li><em>regular_voter<\/em>: Yes if the respondent voted in all or all-but-one of the elections they were eligible for; no otherwise<\/li>\n<\/ul>\n<p>Of the [latex]3,594[\/latex] respondents with a major party affiliation, [latex]1,255[\/latex] were regular voters. Of the [latex]2,242[\/latex] respondents with no major party affiliation, [latex]556[\/latex] were regular voters.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1681\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1681&theme=lumen&iframe_resize_id=ohm1681&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1197-1\">https:\/\/www.whitehouse.gov\/about-the-white-house\/our-government\/elections-and-voting\/ <a href=\"#return-footnote-1197-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-1197-2\">https:\/\/en.wikipedia.org\/wiki\/Political_parties_in_the_United_States <a href=\"#return-footnote-1197-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><li id=\"footnote-1197-3\">Thomson-DeVeaux, A., Mithani, J., &amp; Bronner, L. (2020, October 26). Why many Americans don\u2019t vote. FiveThirtyEight. https:\/\/projects.fivethirtyeight.com\/non-voters-poll-2020-election\/ <a href=\"#return-footnote-1197-3\" class=\"return-footnote\" aria-label=\"Return to footnote 3\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":32,"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\/1197"}],"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\/1197\/revisions"}],"predecessor-version":[{"id":6742,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1197\/revisions\/6742"}],"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\/1197\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1197"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1197"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1197"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1197"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}