{"id":1247,"date":"2023-06-22T02:09:35","date_gmt":"2023-06-22T02:09:35","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/errors-in-hypothesis-testing-apply-it-3\/"},"modified":"2025-05-16T03:41:17","modified_gmt":"2025-05-16T03:41:17","slug":"errors-in-hypothesis-testing-apply-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/errors-in-hypothesis-testing-apply-it-3\/","title":{"raw":"Errors in Hypothesis Testing: Apply It 2","rendered":"Errors in Hypothesis Testing: Apply It 2"},"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;Recognize Type I and Type II errors and their consequences&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Recognize Type I and Type II errors and their consequences.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Type I error<\/h2>\r\n<section class=\"textbox recall\">A\u00a0<strong>Type I<\/strong>\u00a0error occurs when a true null hypothesis is rejected.<\/section>\r\n<section class=\"textbox tryIt\"><span style=\"background-color: initial; font-size: 0.9em; word-spacing: normal;\">[ohm2_question hide_question_numbers=1]951[\/ohm2_question]<\/span><\/section>\r\n<p class=\"para\" style=\"text-align: left;\">Let\u2019s explore the sampling distribution of sample proportions under the null hypothesis.<\/p>\r\n<p class=\"para\" style=\"text-align: center;\"><img class=\"aligncenter wp-image-6878 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/18214841\/NormalDist_Percentile-3.png\" alt=\"A normal distribution curve with a mean of 0.24 and a standard deviation of 0.0177. The 95% confidence interval is marked as being between 0.205 and 0.275.\" width=\"650\" height=\"350\" \/><\/p>\r\n<p>The figure illustrates our hypothesis test decision rule. If the actual sample proportion is greater than [latex]0.275[\/latex] or less than [latex]0.205[\/latex], we would reject the null hypothesis and conclude that there was a change in vaping rates.<\/p>\r\n<p>But, what if the vaping rates did NOT change and you happened to select a sample proportion in the tails portion (shaded light blue) of the distribution? In other words, you selected a \u201clucky\u201d sample that was simply unusual given that the null hypothesis of no change was true ([latex]0.24[\/latex]), which resulted in a small enough P-value to reject the null hypothesis. In this case, you would have committed a <strong>type I error<\/strong>.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1748[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1749[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]953[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Recognize Type I and Type II errors and their consequences&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4609,&quot;3&quot;:{&quot;1&quot;:0},&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Recognize Type I and Type II errors and their consequences.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Type I error<\/h2>\n<section class=\"textbox recall\">A\u00a0<strong>Type I<\/strong>\u00a0error occurs when a true null hypothesis is rejected.<\/section>\n<section class=\"textbox tryIt\"><span style=\"background-color: initial; font-size: 0.9em; word-spacing: normal;\"><iframe loading=\"lazy\" id=\"ohm951\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=951&theme=lumen&iframe_resize_id=ohm951&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/span><\/section>\n<p class=\"para\" style=\"text-align: left;\">Let\u2019s explore the sampling distribution of sample proportions under the null hypothesis.<\/p>\n<p class=\"para\" style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-6878 size-full\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/18214841\/NormalDist_Percentile-3.png\" alt=\"A normal distribution curve with a mean of 0.24 and a standard deviation of 0.0177. The 95% confidence interval is marked as being between 0.205 and 0.275.\" width=\"650\" height=\"350\" \/><\/p>\n<p>The figure illustrates our hypothesis test decision rule. If the actual sample proportion is greater than [latex]0.275[\/latex] or less than [latex]0.205[\/latex], we would reject the null hypothesis and conclude that there was a change in vaping rates.<\/p>\n<p>But, what if the vaping rates did NOT change and you happened to select a sample proportion in the tails portion (shaded light blue) of the distribution? In other words, you selected a \u201clucky\u201d sample that was simply unusual given that the null hypothesis of no change was true ([latex]0.24[\/latex]), which resulted in a small enough P-value to reject the null hypothesis. In this case, you would have committed a <strong>type I error<\/strong>.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1748\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1748&theme=lumen&iframe_resize_id=ohm1748&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1749\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1749&theme=lumen&iframe_resize_id=ohm1749&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm953\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=953&theme=lumen&iframe_resize_id=ohm953&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":29,"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":"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\/1247"}],"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":10,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1247\/revisions"}],"predecessor-version":[{"id":6766,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1247\/revisions\/6766"}],"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\/1247\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1247"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1247"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1247"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1247"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}