{"id":1167,"date":"2023-06-22T01:59:35","date_gmt":"2023-06-22T01:59:35","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-learn-it-1\/"},"modified":"2025-05-16T03:06:35","modified_gmt":"2025-05-16T03:06:35","slug":"confidence-interval-for-proportions-learn-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-learn-it-1\/","title":{"raw":"Confidence Interval for Proportions: Learn It 1","rendered":"Confidence Interval for Proportions: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li class=\"li1\">Check the conditions for creating a confidence interval for population proportion.<\/li>\r\n\t<li class=\"li1\">Describe the connection between the confidence level and the confidence interval.<\/li>\r\n\t<li class=\"li1\">Calculate a confidence interval for a population proportion.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>During an election year, we might hear some news that state <strong>confidence intervals<\/strong> in terms of proportions or percentages.<\/p>\r\n<section class=\"textbox example\">For example, a survey of more than 1,300 adults and about 1,200 registered voters was conducted after President Biden's February 2023 State of the Union address. As shown below, President Biden saw his highest overall approval ratings since March 2022 at [latex]46\\%[\/latex].[footnote]https:\/\/www.npr.org\/2023\/02\/22\/1158538798\/poll-bidens-standing-improves-while-trump-slumps-with-republican-voters[\/footnote]<img class=\"aligncenter wp-image-1939 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/21195515\/Screenshot-2023-07-21-at-12.54.54-PM.png\" alt=\"A graph showing the approval rates for Biden from April 2021 to January 2023. There is a line for Democrats, overall consensus, Independents, and Republicans.\" width=\"944\" height=\"573\" \/><br \/>\r\nDid you notice the fine print?<br \/>\r\n[latex]46\\%[\/latex] is not the true population proportion, but it is a point estimate. This is the reason why they also reported the margin of error for the overall sample.<\/section>\r\n<p>Often, we will not know the true population parameter, so we will need to estimate it. The sample proportion is used as a point estimate of the population proportion.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>point estimate<\/h3>\r\n<p>A <strong>point estimate<\/strong> is a single value based on representative sample data that is a plausible estimate of the population parameter.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>In terms of proportion, the best estimate for the population proportion, [latex]p[\/latex], is the sample proportion.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>We refer to the point estimate for proportions as [latex]\\hat{p}[\/latex].<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1626[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li class=\"li1\">Check the conditions for creating a confidence interval for population proportion.<\/li>\n<li class=\"li1\">Describe the connection between the confidence level and the confidence interval.<\/li>\n<li class=\"li1\">Calculate a confidence interval for a population proportion.<\/li>\n<\/ul>\n<\/section>\n<p>During an election year, we might hear some news that state <strong>confidence intervals<\/strong> in terms of proportions or percentages.<\/p>\n<section class=\"textbox example\">For example, a survey of more than 1,300 adults and about 1,200 registered voters was conducted after President Biden&#8217;s February 2023 State of the Union address. As shown below, President Biden saw his highest overall approval ratings since March 2022 at [latex]46\\%[\/latex].<a class=\"footnote\" title=\"https:\/\/www.npr.org\/2023\/02\/22\/1158538798\/poll-bidens-standing-improves-while-trump-slumps-with-republican-voters\" id=\"return-footnote-1167-1\" href=\"#footnote-1167-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1939 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/21195515\/Screenshot-2023-07-21-at-12.54.54-PM.png\" alt=\"A graph showing the approval rates for Biden from April 2021 to January 2023. There is a line for Democrats, overall consensus, Independents, and Republicans.\" width=\"944\" height=\"573\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/21195515\/Screenshot-2023-07-21-at-12.54.54-PM.png 944w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/21195515\/Screenshot-2023-07-21-at-12.54.54-PM-300x182.png 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/21195515\/Screenshot-2023-07-21-at-12.54.54-PM-768x466.png 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/21195515\/Screenshot-2023-07-21-at-12.54.54-PM-65x39.png 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/21195515\/Screenshot-2023-07-21-at-12.54.54-PM-225x137.png 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/27\/2023\/06\/21195515\/Screenshot-2023-07-21-at-12.54.54-PM-350x212.png 350w\" sizes=\"(max-width: 944px) 100vw, 944px\" \/><br \/>\nDid you notice the fine print?<br \/>\n[latex]46\\%[\/latex] is not the true population proportion, but it is a point estimate. This is the reason why they also reported the margin of error for the overall sample.<\/section>\n<p>Often, we will not know the true population parameter, so we will need to estimate it. The sample proportion is used as a point estimate of the population proportion.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>point estimate<\/h3>\n<p>A <strong>point estimate<\/strong> is a single value based on representative sample data that is a plausible estimate of the population parameter.<\/p>\n<p>&nbsp;<\/p>\n<p>In terms of proportion, the best estimate for the population proportion, [latex]p[\/latex], is the sample proportion.<\/p>\n<p>&nbsp;<\/p>\n<p>We refer to the point estimate for proportions as [latex]\\hat{p}[\/latex].<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1626\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1626&theme=lumen&iframe_resize_id=ohm1626&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1167-1\">https:\/\/www.npr.org\/2023\/02\/22\/1158538798\/poll-bidens-standing-improves-while-trump-slumps-with-republican-voters <a href=\"#return-footnote-1167-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":7,"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\/1167"}],"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":17,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1167\/revisions"}],"predecessor-version":[{"id":6720,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1167\/revisions\/6720"}],"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\/1167\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1167"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1167"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1167"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1167"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}