{"id":1250,"date":"2023-06-22T02:09:37","date_gmt":"2023-06-22T02:09:37","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/two-sample-test-for-proportions-background-youll-need-1\/"},"modified":"2025-05-16T03:30:57","modified_gmt":"2025-05-16T03:30:57","slug":"two-sample-test-for-proportions-background-youll-need-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/two-sample-test-for-proportions-background-youll-need-1\/","title":{"raw":"Module 10: Background You'll Need 6","rendered":"Module 10: Background You&#8217;ll Need 6"},"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;Identify and interpret the difference between sample proportions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4096,&quot;15&quot;:&quot;Calibri&quot;}\">Identify and interpret the difference between sample proportions.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Proportions<\/h2>\r\n<p>A Pew Research Center survey conducted in January 2021 about American adults\u2019 perceptions of the financial impact of the COVID-19 pandemic.[footnote]Horowitz, J. M., Brown, A., &amp; Minkin, R. (2021, March 5). A year into the pandemic, long-term financial impact weighs heavily on many Americans. Pew Research Center. https:\/\/www.pewresearch.org\/social-trends\/2021\/03\/05\/a-year-into-the-pandemic-long-term-financial-impact-weighs-heavily-on-many-americans\/[\/footnote] Note: The survey was conducted in January 2021; the COVID-19 pandemic began in March 2020.<\/p>\r\n<p>The survey randomly selected [latex]10,334[\/latex] U.S. adult respondents. The graphic below shows the percentages of respondents saying that, compared with one year earlier, their financial situations (and that of their families) were better, worse, or about the same.<\/p>\r\n<div><img class=\"aligncenter wp-image-396 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211626\/Screen-Shot-2022-11-02-at-11.45.27-AM.png\" alt=\"xThe figure shows three columns and 5 rows. The first row is a header row and it labels each column \u201cBetter\u201d, \u201cWorse\u201d, and \u201cAbout the same\u201d, respectively. The second row, representing the responses of all adults, shows 30 \u201cbetter\u201d responses, 21 \u201cworse\u201d responses, and 49 \u201cabout the same\u201d responses. The third row, representing the responses of lower income adults, shows 22 \u201cbetter\u201d responses, 31 \u201cworse\u201d responses, and 46 \u201cabout the same\u201d responses. The fourth row, representing the responses of middle income adults, shows 32 \u201cbetter\u201d responses, 18 \u201cworse\u201d responses, and 49 \u201cabout the same\u201d responses. The fifth row, representing the responses of upper income adults, shows 39 \u201cbetter\u201d responses, 11 \u201cworse\u201d responses, and 50 \u201cabout the same\u201d responses. \" width=\"300\" height=\"155\" \/><\/div>\r\n<div><span style=\"font-size: 1rem; text-align: initial;\">Note: Some rows do not add to [latex]100\\%[\/latex] because the shares of respondents who didn\u2019t offer answers are not shown.<\/span><\/div>\r\n<div>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1757[\/ohm2_question]<\/section>\r\n<\/div>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1758[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1759[\/ohm2_question]<\/section>\r\n<p>An inequality is a mathematical statement that compares two expressions using the ideas of greater than or less than. Special symbols are used in these statements. When you read an inequality, read it from left to right\u2014just like reading text on a page.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]958[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1761[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">\r\n<p>[ohm2_question hide_question_numbers=1]1767[\/ohm2_question]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]959[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Identify and interpret the difference between sample proportions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4096,&quot;15&quot;:&quot;Calibri&quot;}\">Identify and interpret the difference between sample proportions.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Proportions<\/h2>\n<p>A Pew Research Center survey conducted in January 2021 about American adults\u2019 perceptions of the financial impact of the COVID-19 pandemic.<a class=\"footnote\" title=\"Horowitz, J. M., Brown, A., &amp; Minkin, R. (2021, March 5). A year into the pandemic, long-term financial impact weighs heavily on many Americans. Pew Research Center. https:\/\/www.pewresearch.org\/social-trends\/2021\/03\/05\/a-year-into-the-pandemic-long-term-financial-impact-weighs-heavily-on-many-americans\/\" id=\"return-footnote-1250-1\" href=\"#footnote-1250-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> Note: The survey was conducted in January 2021; the COVID-19 pandemic began in March 2020.<\/p>\n<p>The survey randomly selected [latex]10,334[\/latex] U.S. adult respondents. The graphic below shows the percentages of respondents saying that, compared with one year earlier, their financial situations (and that of their families) were better, worse, or about the same.<\/p>\n<div><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-396 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211626\/Screen-Shot-2022-11-02-at-11.45.27-AM.png\" alt=\"xThe figure shows three columns and 5 rows. The first row is a header row and it labels each column \u201cBetter\u201d, \u201cWorse\u201d, and \u201cAbout the same\u201d, respectively. The second row, representing the responses of all adults, shows 30 \u201cbetter\u201d responses, 21 \u201cworse\u201d responses, and 49 \u201cabout the same\u201d responses. The third row, representing the responses of lower income adults, shows 22 \u201cbetter\u201d responses, 31 \u201cworse\u201d responses, and 46 \u201cabout the same\u201d responses. The fourth row, representing the responses of middle income adults, shows 32 \u201cbetter\u201d responses, 18 \u201cworse\u201d responses, and 49 \u201cabout the same\u201d responses. The fifth row, representing the responses of upper income adults, shows 39 \u201cbetter\u201d responses, 11 \u201cworse\u201d responses, and 50 \u201cabout the same\u201d responses.\" width=\"300\" height=\"155\" \/><\/div>\n<div><span style=\"font-size: 1rem; text-align: initial;\">Note: Some rows do not add to [latex]100\\%[\/latex] because the shares of respondents who didn\u2019t offer answers are not shown.<\/span><\/div>\n<div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1757\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1757&theme=lumen&iframe_resize_id=ohm1757&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1758\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1758&theme=lumen&iframe_resize_id=ohm1758&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1759\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1759&theme=lumen&iframe_resize_id=ohm1759&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>An inequality is a mathematical statement that compares two expressions using the ideas of greater than or less than. Special symbols are used in these statements. When you read an inequality, read it from left to right\u2014just like reading text on a page.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm958\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=958&theme=lumen&iframe_resize_id=ohm958&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1761\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1761&theme=lumen&iframe_resize_id=ohm1761&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\">\n<iframe loading=\"lazy\" id=\"ohm1767\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1767&theme=lumen&iframe_resize_id=ohm1767&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><br \/>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm959\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=959&theme=lumen&iframe_resize_id=ohm959&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1250-1\">Horowitz, J. M., Brown, A., &amp; Minkin, R. (2021, March 5). A year into the pandemic, long-term financial impact weighs heavily on many Americans. Pew Research Center. https:\/\/www.pewresearch.org\/social-trends\/2021\/03\/05\/a-year-into-the-pandemic-long-term-financial-impact-weighs-heavily-on-many-americans\/ <a href=\"#return-footnote-1250-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":7,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1205,"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\/1250"}],"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":11,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1250\/revisions"}],"predecessor-version":[{"id":6748,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1250\/revisions\/6748"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1205"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1250\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1250"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1250"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1250"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1250"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}