{"id":1178,"date":"2023-06-22T01:59:43","date_gmt":"2023-06-22T01:59:43","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-continued-background-youll-need-2\/"},"modified":"2024-02-21T22:29:43","modified_gmt":"2024-02-21T22:29:43","slug":"confidence-interval-for-proportions-continued-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-proportions-continued-background-youll-need-2\/","title":{"raw":"Module 9: Background You'll Need 3","rendered":"Module 9: Background You&#8217;ll Need 3"},"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;Calculate the mean and standard error for a sample proportion&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4096,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate the mean and standard error for a sample proportion.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Previously, we learned about the connections between a population and the sampling distribution of a sample proportion from that population. That is, when taking many random samples of size [latex] n [\/latex] from a population distribution with proportion [latex]p[\/latex], the mean of the distribution of sample proportions is [latex]p[\/latex] and the standard deviation of the distribution of sample proportions is [latex] \\sqrt{\\frac{p(1-p)}{n}} [\/latex].<\/p>\r\n<p>However, we rarely (if ever) know the true value of the population proportion. So instead, we can estimate the mean and standard deviation of the sampling distribution.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>The estimated mean and standard deviation of the sampling distribution of sample proportions<\/h3>\r\n<ul>\r\n\t<li>Estimate for the mean of sample proportions = [latex]\\hat{p}[\/latex] = sample proportion<\/li>\r\n\t<li>Estimate for the standard deviation of sample proportions (a.k.a., standard error) = [latex]SE = \\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}[\/latex]<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1635[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1636[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate the mean and standard error for a sample proportion&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4096,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate the mean and standard error for a sample proportion.<\/span><\/li>\n<\/ul>\n<\/section>\n<p>Previously, we learned about the connections between a population and the sampling distribution of a sample proportion from that population. That is, when taking many random samples of size [latex]n[\/latex] from a population distribution with proportion [latex]p[\/latex], the mean of the distribution of sample proportions is [latex]p[\/latex] and the standard deviation of the distribution of sample proportions is [latex]\\sqrt{\\frac{p(1-p)}{n}}[\/latex].<\/p>\n<p>However, we rarely (if ever) know the true value of the population proportion. So instead, we can estimate the mean and standard deviation of the sampling distribution.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>The estimated mean and standard deviation of the sampling distribution of sample proportions<\/h3>\n<ul>\n<li>Estimate for the mean of sample proportions = [latex]\\hat{p}[\/latex] = sample proportion<\/li>\n<li>Estimate for the standard deviation of sample proportions (a.k.a., standard error) = [latex]SE = \\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}[\/latex]<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1635\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1635&theme=lumen&iframe_resize_id=ohm1635&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1636\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1636&theme=lumen&iframe_resize_id=ohm1636&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":4,"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":"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\/1178"}],"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":6,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1178\/revisions"}],"predecessor-version":[{"id":5607,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1178\/revisions\/5607"}],"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\/1178\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1178"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1178"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1178"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1178"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}