{"id":1415,"date":"2023-06-22T02:22:57","date_gmt":"2023-06-22T02:22:57","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-of-homogeneity-learn-it-4\/"},"modified":"2023-10-20T20:45:14","modified_gmt":"2023-10-20T20:45:14","slug":"chi-square-test-of-homogeneity-learn-it-4","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/chi-square-test-of-homogeneity-learn-it-4\/","title":{"raw":"Chi-Square Test of Homogeneity \u2013 Learn It 4","rendered":"Chi-Square Test of Homogeneity \u2013 Learn It 4"},"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 of homogeneity&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 of homogeneity<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Certain conditions and assumptions must be met before using the chi-square distribution to conduct the hypothesis testing.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>conditions for a [latex]\\chi^2[\/latex] test of homogeneity<\/h3>\r\n<ol>\r\n\t<li><strong>Appropriate Data and Variables<\/strong>: This is not an official condition, but it is important to make sure that we are dealing with data that give the counts for each value of a categorical variable. That categorical variable should be measured for a sample from each population of interest.<\/li>\r\n\t<li><strong>Independence\/Randomness Condition<\/strong>: The samples from our populations should be independent, random samples or independent samples that can be considered representative of the respective populations.<\/li>\r\n\t<li><strong>Large Sample Sizes Condition<\/strong>: The sample sizes need to be large enough so that the expected count in each cell is at least five.<\/li>\r\n<\/ol>\r\n<\/section>\r\n<p>Recall that we are considering the question of whether the distributions of flight status are the same among the flights of the three airlines.<\/p>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>&nbsp;<\/td>\r\n<td><strong>On-Time Flights<\/strong><\/td>\r\n<td><strong>Delayed Flights<\/strong><\/td>\r\n<td><strong>Canceled Flights<\/strong><\/td>\r\n<td><strong>Diverted Flights<\/strong><\/td>\r\n<td><strong>Total<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>American Airlines<\/strong><\/td>\r\n<td>42,600<\/td>\r\n<td>4,657<\/td>\r\n<td>296<\/td>\r\n<td>95<\/td>\r\n<td>47,648<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Delta Airlines<\/strong><\/td>\r\n<td>51,620<\/td>\r\n<td>4,030<\/td>\r\n<td>150<\/td>\r\n<td>56<\/td>\r\n<td>55,856<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Southwest Airlines<\/strong><\/td>\r\n<td>69,384<\/td>\r\n<td>9,280<\/td>\r\n<td>1,782<\/td>\r\n<td>128<\/td>\r\n<td>80,574<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>Total <\/strong><\/td>\r\n<td>163,604<\/td>\r\n<td>17,967<\/td>\r\n<td>2,228<\/td>\r\n<td>279<\/td>\r\n<td>184,078<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1 ]2441[\/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 of homogeneity&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 of homogeneity<\/span><\/li>\n<\/ul>\n<\/section>\n<p>Certain conditions and assumptions must be met before using the chi-square distribution to conduct the hypothesis testing.<\/p>\n<section class=\"textbox keyTakeaway\">\n<h3>conditions for a [latex]\\chi^2[\/latex] test of homogeneity<\/h3>\n<ol>\n<li><strong>Appropriate Data and Variables<\/strong>: This is not an official condition, but it is important to make sure that we are dealing with data that give the counts for each value of a categorical variable. That categorical variable should be measured for a sample from each population of interest.<\/li>\n<li><strong>Independence\/Randomness Condition<\/strong>: The samples from our populations should be independent, random samples or independent samples that can be considered representative of the respective populations.<\/li>\n<li><strong>Large Sample Sizes Condition<\/strong>: The sample sizes need to be large enough so that the expected count in each cell is at least five.<\/li>\n<\/ol>\n<\/section>\n<p>Recall that we are considering the question of whether the distributions of flight status are the same among the flights of the three airlines.<\/p>\n<table>\n<tbody>\n<tr>\n<td>&nbsp;<\/td>\n<td><strong>On-Time Flights<\/strong><\/td>\n<td><strong>Delayed Flights<\/strong><\/td>\n<td><strong>Canceled Flights<\/strong><\/td>\n<td><strong>Diverted Flights<\/strong><\/td>\n<td><strong>Total<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>American Airlines<\/strong><\/td>\n<td>42,600<\/td>\n<td>4,657<\/td>\n<td>296<\/td>\n<td>95<\/td>\n<td>47,648<\/td>\n<\/tr>\n<tr>\n<td><strong>Delta Airlines<\/strong><\/td>\n<td>51,620<\/td>\n<td>4,030<\/td>\n<td>150<\/td>\n<td>56<\/td>\n<td>55,856<\/td>\n<\/tr>\n<tr>\n<td><strong>Southwest Airlines<\/strong><\/td>\n<td>69,384<\/td>\n<td>9,280<\/td>\n<td>1,782<\/td>\n<td>128<\/td>\n<td>80,574<\/td>\n<\/tr>\n<tr>\n<td><strong>Total <\/strong><\/td>\n<td>163,604<\/td>\n<td>17,967<\/td>\n<td>2,228<\/td>\n<td>279<\/td>\n<td>184,078<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2441\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2441&theme=lumen&iframe_resize_id=ohm2441&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":22,"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":"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\/1415"}],"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":3,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1415\/revisions"}],"predecessor-version":[{"id":3949,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1415\/revisions\/3949"}],"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\/1415\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1415"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1415"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1415"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1415"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}