{"id":1407,"date":"2023-06-22T02:22:50","date_gmt":"2023-06-22T02:22:50","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-for-goodness-of-fit-apply-it-1\/"},"modified":"2025-05-16T23:39:33","modified_gmt":"2025-05-16T23:39:33","slug":"chi-square-test-for-goodness-of-fit-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-for-goodness-of-fit-apply-it-1\/","title":{"raw":"Chi-Square Test for Goodness of Fit \u2013 Apply It 1","rendered":"Chi-Square Test for Goodness of Fit \u2013 Apply It 1"},"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;Complete a chi-square test for goodness of fit and write its conclusion in context of the problem&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Complete a chi-square test for goodness of fit and write its conclusion in context of the problem<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Is it Equitable?<\/h2>\r\n<p><img class=\"alignright wp-image-1479\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193813\/Vaccine-development-rafiki.png\" alt=\"Animated image of three people trying to move a giant syringe.\" width=\"226\" height=\"226\" \/><\/p>\r\n<p>During public health crises, governments often aim to distribute resources and aid to citizens equitably. However, in practice, this may not always be the case. We will explore some mock data about vaccine distribution in New York during a pandemic.<\/p>\r\n<p>Imagine a vaccine for a pandemic is produced, but there is a limited supply. Although the government promises that the vaccine will be distributed equitably, New Yorkers wonder whether the government is preferentially distributing it to wealthy individuals.<\/p>\r\n<p>The State of New York claims that each county receives a number of vaccines that is proportional to its population size.<\/p>\r\n<p>An independent inspector is granted access to obtain a random sample of vaccine box shipping labels in a warehouse shipping to only three New York counties: the Bronx, Queens, and Westchester. The median income is highest in Westchester County, followed by Queens, and finally the Bronx. Below are the populations of all three counties (as of 2019, according to the U.S. Census Bureau).<\/p>\r\n<div align=\"center\">\r\n<table style=\"width: 229px;\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 144.469px;\"><strong>County<\/strong><\/td>\r\n<td style=\"width: 153.031px;\"><strong>Population Size<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 144.469px;\">Queens<\/td>\r\n<td style=\"width: 153.031px;\">2,287,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 144.469px;\">Bronx<\/td>\r\n<td style=\"width: 153.031px;\">1,435,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 144.469px;\">Westchester<\/td>\r\n<td style=\"width: 153.031px;\">968,000<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2358[\/ohm2_question]<\/section>\r\n<p class=\"student12ptnumberlist\">The independent inspector collects a random sample of 500 shipping labels for vaccine boxes being distributed by the warehouse (all boxes have an equal number of vaccine doses). The independent inspector would like to test if there\u2019s convincing evidence against the claim that vaccine shipments are proportional to each county\u2019s population size using a <b>chi-square test for goodness of fit<\/b>.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2359[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete a chi-square test for goodness of fit and write its conclusion in context of the problem&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12801,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Complete a chi-square test for goodness of fit and write its conclusion in context of the problem<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Is it Equitable?<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright wp-image-1479\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2023\/04\/24193813\/Vaccine-development-rafiki.png\" alt=\"Animated image of three people trying to move a giant syringe.\" width=\"226\" height=\"226\" \/><\/p>\n<p>During public health crises, governments often aim to distribute resources and aid to citizens equitably. However, in practice, this may not always be the case. We will explore some mock data about vaccine distribution in New York during a pandemic.<\/p>\n<p>Imagine a vaccine for a pandemic is produced, but there is a limited supply. Although the government promises that the vaccine will be distributed equitably, New Yorkers wonder whether the government is preferentially distributing it to wealthy individuals.<\/p>\n<p>The State of New York claims that each county receives a number of vaccines that is proportional to its population size.<\/p>\n<p>An independent inspector is granted access to obtain a random sample of vaccine box shipping labels in a warehouse shipping to only three New York counties: the Bronx, Queens, and Westchester. The median income is highest in Westchester County, followed by Queens, and finally the Bronx. Below are the populations of all three counties (as of 2019, according to the U.S. Census Bureau).<\/p>\n<div style=\"margin: auto;\">\n<table style=\"width: 229px;\">\n<tbody>\n<tr>\n<td style=\"width: 144.469px;\"><strong>County<\/strong><\/td>\n<td style=\"width: 153.031px;\"><strong>Population Size<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 144.469px;\">Queens<\/td>\n<td style=\"width: 153.031px;\">2,287,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 144.469px;\">Bronx<\/td>\n<td style=\"width: 153.031px;\">1,435,000<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 144.469px;\">Westchester<\/td>\n<td style=\"width: 153.031px;\">968,000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2358\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2358&theme=lumen&iframe_resize_id=ohm2358&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p class=\"student12ptnumberlist\">The independent inspector collects a random sample of 500 shipping labels for vaccine boxes being distributed by the warehouse (all boxes have an equal number of vaccine doses). The independent inspector would like to test if there\u2019s convincing evidence against the claim that vaccine shipments are proportional to each county\u2019s population size using a <b>chi-square test for goodness of fit<\/b>.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2359\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2359&theme=lumen&iframe_resize_id=ohm2359&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":16,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1388,"module-header":"apply_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\/1407"}],"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\/1407\/revisions"}],"predecessor-version":[{"id":6870,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1407\/revisions\/6870"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1388"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1407\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1407"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1407"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1407"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1407"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}