{"id":1291,"date":"2023-06-22T02:13:22","date_gmt":"2023-06-22T02:13:22","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-a-population-mean-background-youll-need-2-2\/"},"modified":"2024-02-07T18:23:45","modified_gmt":"2024-02-07T18:23:45","slug":"confidence-interval-for-a-population-mean-background-youll-need-2-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-a-population-mean-background-youll-need-2-2\/","title":{"raw":"Module 11: Background You'll Need 4","rendered":"Module 11: Background You&#8217;ll Need 4"},"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;Compare values as included or excluded from a given interval&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4096,&quot;15&quot;:&quot;Calibri&quot;}\">Compare values as included or excluded from a given interval.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox example\">Consider the interval that contains all the numbers between [latex]42[\/latex] and [latex]58[\/latex].<br \/>\r\n[reveal-answer q=\"183210\"]There are several ways to represent an interval.[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"183210\"]\r\n\r\n<ul>\r\n\t<li>Number line:<\/li>\r\n<\/ul>\r\n<p><img class=\"aligncenter wp-image-6988 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23181841\/Picture1-13.png\" alt=\"A number line marked from 42 to 58.\" width=\"936\" height=\"92\" \/><\/p>\r\n<ul>\r\n\t<li>Interval notation: [latex](42, 58)[\/latex]<\/li>\r\n\t<li>[latex]\\pm[\/latex] notation: [latex]50 \\pm 8[\/latex]<\/li>\r\n<\/ul>\r\n<p style=\"padding-left: 40px;\">Note: To get [latex]50[\/latex], find the midpoint between 42 and 58, which is just the average of the two endpoints = [latex]\\frac{42+58}{2}=50[\/latex].[\/hidden-answer]<\/p>\r\n<p>Give an example of a number that is in this interval.<\/p>\r\n<p>[reveal-answer q=\"90660\"]Show answer[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"90660\"]There are infinitely many numbers that can be within this interval. For example: [latex]43, 45.5, 50\\frac{2}{3}, 57.99[\/latex].[\/hidden-answer]<\/p>\r\n<p>Give an example of a number that is not in this interval.<\/p>\r\n<p>[reveal-answer q=\"90661\"]Show answer[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"90661\"]There are infinitely many numbers that are outside of this interval. In fact, any numbers below [latex]42[\/latex] or above [latex]58[\/latex] will be correct. For example: [latex]-15, 0, 40\\frac{2}{3}, 58.01,12345.67[\/latex].[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\"><iframe id=\"ohm1800\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq2.php?id=1800&amp;theme=oea&amp;iframe_resize_id=ohm1800&amp;show_question_numbers\" width=\"100%\" height=\"600\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><\/section>\r\n<section class=\"textbox tryIt\"><iframe id=\"ohm1801\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq2.php?id=1801&amp;theme=oea&amp;iframe_resize_id=ohm1801&amp;show_question_numbers\" width=\"100%\" height=\"600\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Compare values as included or excluded from a given interval&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4096,&quot;15&quot;:&quot;Calibri&quot;}\">Compare values as included or excluded from a given interval.<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox example\">Consider the interval that contains all the numbers between [latex]42[\/latex] and [latex]58[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q183210\">There are several ways to represent an interval.<\/button><\/p>\n<div id=\"q183210\" class=\"hidden-answer\" style=\"display: none\">\n<ul>\n<li>Number line:<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-6988 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23181841\/Picture1-13.png\" alt=\"A number line marked from 42 to 58.\" width=\"936\" height=\"92\" \/><\/p>\n<ul>\n<li>Interval notation: [latex](42, 58)[\/latex]<\/li>\n<li>[latex]\\pm[\/latex] notation: [latex]50 \\pm 8[\/latex]<\/li>\n<\/ul>\n<p style=\"padding-left: 40px;\">Note: To get [latex]50[\/latex], find the midpoint between 42 and 58, which is just the average of the two endpoints = [latex]\\frac{42+58}{2}=50[\/latex].<\/div>\n<\/div>\n<p>Give an example of a number that is in this interval.<\/p>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q90660\">Show answer<\/button><\/p>\n<div id=\"q90660\" class=\"hidden-answer\" style=\"display: none\">There are infinitely many numbers that can be within this interval. For example: [latex]43, 45.5, 50\\frac{2}{3}, 57.99[\/latex].<\/div>\n<\/div>\n<p>Give an example of a number that is not in this interval.<\/p>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q90661\">Show answer<\/button><\/p>\n<div id=\"q90661\" class=\"hidden-answer\" style=\"display: none\">There are infinitely many numbers that are outside of this interval. In fact, any numbers below [latex]42[\/latex] or above [latex]58[\/latex] will be correct. For example: [latex]-15, 0, 40\\frac{2}{3}, 58.01,12345.67[\/latex].<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1800\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq2.php?id=1800&amp;theme=oea&amp;iframe_resize_id=ohm1800&amp;show_question_numbers\" width=\"100%\" height=\"600\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1801\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq2.php?id=1801&amp;theme=oea&amp;iframe_resize_id=ohm1801&amp;show_question_numbers\" width=\"100%\" height=\"600\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":5,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1268,"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\/1291"}],"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":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1291\/revisions"}],"predecessor-version":[{"id":5453,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1291\/revisions\/5453"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1268"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1291\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1291"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1291"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1291"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}