{"id":1188,"date":"2023-06-22T01:59:51","date_gmt":"2023-06-22T01:59:51","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sample-size-for-proportions-learn-it-2\/"},"modified":"2024-02-29T20:34:30","modified_gmt":"2024-02-29T20:34:30","slug":"sample-size-for-proportions-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sample-size-for-proportions-learn-it-2\/","title":{"raw":"Sample Size for Proportions: Learn It 2","rendered":"Sample Size for Proportions: Learn It 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li class=\"li1\">Find the required sample size for a desired margin of error and population's confidence interval.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox recall\">The equation for <strong>margin of error<\/strong> ([latex] ME [\/latex]) is [latex] ME = z^{*} \\cdot (\\text{standard error}) [\/latex]\r\n\r\n<p style=\"padding-left: 40px;\">The equation for <strong>standard error<\/strong> for a proportion is [latex] \\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}} [\/latex], where [latex] \\hat{p} [\/latex] is the sample proportion and [latex] n [\/latex] is the sample size.<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1043[\/ohm2_question]<\/section>\r\n<p>Let's explore how sample size affects the margin of error.<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/inference_prop\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\r\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/inference_prop\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1669[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li class=\"li1\">Find the required sample size for a desired margin of error and population&#8217;s confidence interval.<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox recall\">The equation for <strong>margin of error<\/strong> ([latex]ME[\/latex]) is [latex]ME = z^{*} \\cdot (\\text{standard error})[\/latex]<\/p>\n<p style=\"padding-left: 40px;\">The equation for <strong>standard error<\/strong> for a proportion is [latex]\\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}[\/latex], where [latex]\\hat{p}[\/latex] is the sample proportion and [latex]n[\/latex] is the sample size.<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1043\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1043&theme=lumen&iframe_resize_id=ohm1043&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Let&#8217;s explore how sample size affects the margin of error.<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/inference_prop\/\" width=\"100%\" height=\"850\"><\/iframe><\/p>\n<p>[<a href=\"https:\/\/lumen-learning.shinyapps.io\/inference_prop\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1669\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1669&theme=lumen&iframe_resize_id=ohm1669&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":23,"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\/1188"}],"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":5,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1188\/revisions"}],"predecessor-version":[{"id":5768,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1188\/revisions\/5768"}],"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\/1188\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1188"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1188"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1188"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1188"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}