{"id":1172,"date":"2023-06-22T01:59:39","date_gmt":"2023-06-22T01:59:39","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-learn-it-5\/"},"modified":"2025-05-16T03:08:29","modified_gmt":"2025-05-16T03:08:29","slug":"confidence-interval-for-proportions-learn-it-5","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-learn-it-5\/","title":{"raw":"Confidence Interval for Proportions: Learn It 5","rendered":"Confidence Interval for Proportions: Learn It 5"},"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<h2>Confidence Interval for a Population Proportion<\/h2>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<p>[embed]https:\/\/www.youtube.com\/watch?v=iWYPFFFu-5Q[\/embed]<\/p>\r\n<p>&nbsp;<\/p>\r\n<\/section>\r\n<p>To obtain the confidence interval for a proportion, you need:<\/p>\r\n<ul>\r\n\t<li>Point estimate of a proportion, [latex]\\hat{p}[\/latex]<\/li>\r\n\t<li>Margin of error, [latex]ME = z^{*} \\cdot (\\text{standard error})[\/latex]\r\n\r\n<ul>\r\n\t<li>standard error = [latex]\\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}} [\/latex]<\/li>\r\n\t<li>[latex]z^{*}[\/latex] is the point on the standard normal distribution such that the proportion of area under the curve between [latex]\u2212z^{*}[\/latex] and [latex]+z^{*}[\/latex] is [latex] C[\/latex], the confidence level.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3><strong>confidence interval for a population proportion<\/strong><\/h3>\r\n<p>In general, the end points of a confidence interval are:<\/p>\r\n<p style=\"text-align: center;\">point estimate \u00b1 margin of error<\/p>\r\n<p>&nbsp;<\/p>\r\n<p><strong>The confidence interval for a population proportion<\/strong> is:<\/p>\r\n<p style=\"text-align: center;\">[latex]\\hat{p} \\pm z^{*} \\cdot\\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}} [\/latex]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1631[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1632[\/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<h2>Confidence Interval for a Population Proportion<\/h2>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Rise and Shine\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/iWYPFFFu-5Q?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<\/section>\n<p>To obtain the confidence interval for a proportion, you need:<\/p>\n<ul>\n<li>Point estimate of a proportion, [latex]\\hat{p}[\/latex]<\/li>\n<li>Margin of error, [latex]ME = z^{*} \\cdot (\\text{standard error})[\/latex]\n<ul>\n<li>standard error = [latex]\\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}[\/latex]<\/li>\n<li>[latex]z^{*}[\/latex] is the point on the standard normal distribution such that the proportion of area under the curve between [latex]\u2212z^{*}[\/latex] and [latex]+z^{*}[\/latex] is [latex]C[\/latex], the confidence level.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<section class=\"textbox keyTakeaway\">\n<h3><strong>confidence interval for a population proportion<\/strong><\/h3>\n<p>In general, the end points of a confidence interval are:<\/p>\n<p style=\"text-align: center;\">point estimate \u00b1 margin of error<\/p>\n<p>&nbsp;<\/p>\n<p><strong>The confidence interval for a population proportion<\/strong> is:<\/p>\n<p style=\"text-align: center;\">[latex]\\hat{p} \\pm z^{*} \\cdot\\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}[\/latex]<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1631\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1631&theme=lumen&iframe_resize_id=ohm1631&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1632\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1632&theme=lumen&iframe_resize_id=ohm1632&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":11,"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\/1172"}],"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":10,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1172\/revisions"}],"predecessor-version":[{"id":6723,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1172\/revisions\/6723"}],"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\/1172\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1172"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1172"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1172"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}