{"id":1186,"date":"2023-06-22T01:59:49","date_gmt":"2023-06-22T01:59:49","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sample-size-for-proportions-background-youll-need-2\/"},"modified":"2025-05-16T03:05:27","modified_gmt":"2025-05-16T03:05:27","slug":"sample-size-for-proportions-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sample-size-for-proportions-background-youll-need-2\/","title":{"raw":"Module 9: Background You'll Need 5","rendered":"Module 9: Background You&#8217;ll Need 5"},"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;Describe how a change in the numerator or denominator of a fraction changes the size of the number&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4096,&quot;15&quot;:&quot;Calibri&quot;}\">Describe how a change in the numerator or denominator of a fraction changes the size of the number.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Proportion of Successes and Failures<\/h2>\r\n<p>In research, when using proportions, we can never have a result higher than [latex] \\hat{p} = 1 [\/latex].<\/p>\r\n<p>Consider our dairy farm example. If 100 people are surveyed, there is no way we can get more than 100 \u201cyes\u201d answers.<\/p>\r\n<p>This allows us to determine the proportion of failures for any given value of [latex] \\hat{p} [\/latex] (the proportion of successes in the sample) using the formula [latex] 1 - \\hat{p} [\/latex].<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1657[\/ohm2_question]<\/section>\r\n<p>It is also important to understand how changing the numerator or denominator of a fraction or proportion changes the overall value.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1658[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Describe how a change in the numerator or denominator of a fraction changes the size of the number&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4096,&quot;15&quot;:&quot;Calibri&quot;}\">Describe how a change in the numerator or denominator of a fraction changes the size of the number.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Proportion of Successes and Failures<\/h2>\n<p>In research, when using proportions, we can never have a result higher than [latex]\\hat{p} = 1[\/latex].<\/p>\n<p>Consider our dairy farm example. If 100 people are surveyed, there is no way we can get more than 100 \u201cyes\u201d answers.<\/p>\n<p>This allows us to determine the proportion of failures for any given value of [latex]\\hat{p}[\/latex] (the proportion of successes in the sample) using the formula [latex]1 - \\hat{p}[\/latex].<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1657\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1657&theme=lumen&iframe_resize_id=ohm1657&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>It is also important to understand how changing the numerator or denominator of a fraction or proportion changes the overall value.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1658\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1658&theme=lumen&iframe_resize_id=ohm1658&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":6,"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\/1186"}],"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\/1186\/revisions"}],"predecessor-version":[{"id":6718,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1186\/revisions\/6718"}],"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\/1186\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1186"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1186"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1186"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}