{"id":1166,"date":"2023-06-22T01:59:34","date_gmt":"2023-06-22T01:59:34","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-background-youll-need-1\/"},"modified":"2025-05-16T03:04:22","modified_gmt":"2025-05-16T03:04:22","slug":"confidence-interval-for-proportions-background-youll-need-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-background-youll-need-1\/","title":{"raw":"Module 9: Background You'll Need 1","rendered":"Module 9: Background You&#8217;ll Need 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;Represent intervals on a numberline and using plus-minus notation&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;}\">Represent intervals on a number line and using plus\/minus notation.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Intervals<\/h2>\r\n<p><strong>Interval notation<\/strong> is a way of describing sets that include all real numbers between a lower bound and an upper bound. These bounds may or may not be included in the set. The endpoint values are listed between brackets or parentheses. A square bracket indicates inclusion in the set, and a parenthesis indicates exclusion from the set.<\/p>\r\n<section class=\"textbox recall\">\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 33.3333%;\"><strong>Inequality<\/strong><\/td>\r\n<td style=\"width: 33.3333%;\"><strong>Words<\/strong><\/td>\r\n<td style=\"width: 33.3333%;\"><strong>Interval Notation<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">[latex]{a}\\lt{x}\\lt{ b}[\/latex]<\/td>\r\n<td style=\"width: 33.3333%;\">All real numbers between <em>a <\/em>and <em>b<\/em><\/td>\r\n<td style=\"width: 33.3333%;\">[latex]\\left(a,b\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section>\r\n<section class=\"textbox example\">Suppose you want to buy a pair of jeans. At department stores, the average cost of jeans may be $30. Suppose at some stores the cost may be up to $5 over that cost, while at other stores the cost may be up to $5 lower than that cost. We can write this using [latex] \\pm [\/latex] notation as $30 [latex] \\pm [\/latex] $5. If we subtract 5 from 30, we get $25 [latex] (30 \u2013 5 = 25) [\/latex], and if we add 5 to 30, we get $35 [latex] (30 + 5 = 35) [\/latex].\r\n\r\n<p>This makes our cost range for department store jeans $25 to $35. In interval notation, this can be represented as [latex] ($25, $35) [\/latex].<\/p>\r\n<p>$25 is the <strong>lower<\/strong> <strong>bound<\/strong> of the cost interval, and $35 is the <strong>u<\/strong><strong>pper bound<\/strong> of the cost interval.<br \/>\r\nThis can also be represented on a number line by putting a dot in the center at 30 and drawing a line that extends 5 in both directions.<\/p>\r\n<p><img class=\"aligncenter wp-image-25 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211532\/Picture1.png\" alt=\"A number line with 25 marked as the lower bound and 35 marked as the upper bound. 30 is marked as the midpoint.\" width=\"300\" height=\"31\" \/><\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question]1614[\/ohm2_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question]1615[\/ohm2_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question]1616[\/ohm2_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question]1618[\/ohm2_question]<\/p>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Represent intervals on a numberline and using plus-minus notation&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;}\">Represent intervals on a number line and using plus\/minus notation.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Intervals<\/h2>\n<p><strong>Interval notation<\/strong> is a way of describing sets that include all real numbers between a lower bound and an upper bound. These bounds may or may not be included in the set. The endpoint values are listed between brackets or parentheses. A square bracket indicates inclusion in the set, and a parenthesis indicates exclusion from the set.<\/p>\n<section class=\"textbox recall\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%;\"><strong>Inequality<\/strong><\/td>\n<td style=\"width: 33.3333%;\"><strong>Words<\/strong><\/td>\n<td style=\"width: 33.3333%;\"><strong>Interval Notation<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">[latex]{a}\\lt{x}\\lt{ b}[\/latex]<\/td>\n<td style=\"width: 33.3333%;\">All real numbers between <em>a <\/em>and <em>b<\/em><\/td>\n<td style=\"width: 33.3333%;\">[latex]\\left(a,b\\right)[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section class=\"textbox example\">Suppose you want to buy a pair of jeans. At department stores, the average cost of jeans may be $30. Suppose at some stores the cost may be up to $5 over that cost, while at other stores the cost may be up to $5 lower than that cost. We can write this using [latex]\\pm[\/latex] notation as $30 [latex]\\pm[\/latex] $5. If we subtract 5 from 30, we get $25 [latex](30 \u2013 5 = 25)[\/latex], and if we add 5 to 30, we get $35 [latex](30 + 5 = 35)[\/latex].<\/p>\n<p>This makes our cost range for department store jeans $25 to $35. In interval notation, this can be represented as [latex]($25, $35)[\/latex].<\/p>\n<p>$25 is the <strong>lower<\/strong> <strong>bound<\/strong> of the cost interval, and $35 is the <strong>u<\/strong><strong>pper bound<\/strong> of the cost interval.<br \/>\nThis can also be represented on a number line by putting a dot in the center at 30 and drawing a line that extends 5 in both directions.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-25 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211532\/Picture1.png\" alt=\"A number line with 25 marked as the lower bound and 35 marked as the upper bound. 30 is marked as the midpoint.\" width=\"300\" height=\"31\" \/><\/p>\n<\/section>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm1614\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1614&theme=lumen&iframe_resize_id=ohm1614&source=tnh&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm1615\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1615&theme=lumen&iframe_resize_id=ohm1615&source=tnh&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm1616\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1616&theme=lumen&iframe_resize_id=ohm1616&source=tnh&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm1618\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1618&theme=lumen&iframe_resize_id=ohm1618&source=tnh&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n","protected":false},"author":8,"menu_order":2,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"part":1163,"module-header":"background_you_need","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\/1166"}],"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\/1166\/revisions"}],"predecessor-version":[{"id":6716,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1166\/revisions\/6716"}],"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\/1166\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1166"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1166"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1166"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}