{"id":1216,"date":"2023-06-22T02:09:13","date_gmt":"2023-06-22T02:09:13","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypotheses-dig-deeper\/"},"modified":"2025-05-16T03:34:49","modified_gmt":"2025-05-16T03:34:49","slug":"null-and-alternative-hypotheses-dig-deeper","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypotheses-dig-deeper\/","title":{"raw":"Null and Alternative Hypotheses: Fresh Take","rendered":"Null and Alternative Hypotheses: Fresh Take"},"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;Write a null and alternative hypothesis for a hypothesis test&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;}\">Write a null and alternative hypothesis for a hypothesis test.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Decide if a sample statistic provides enough evidence to reject the null hypothesis&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;}\">Decide if a sample statistic provides enough evidence to reject the null hypothesis.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox recall\">The <strong>null hypothesis<\/strong>, [latex] H_{0} [\/latex], is what we assume to be true to begin with. This can often be considered the status quo, and as a result, if you cannot accept the null, it requires some action.\r\n\r\n<ul>\r\n\t<li>For proportion, our parameter is population proportion, denoted [latex]p[\/latex], therefore our null hypothesis is [latex]H_0: p = \\text{null value}[\/latex]<\/li>\r\n<\/ul>\r\n<p>The <strong>alternative hypothesis<\/strong>, [latex] H_{A} [\/latex], is what we consider to be plausible if the null hypothesis is false. This is usually what the researcher is trying to prove.<\/p>\r\n<ul>\r\n\t<li>The alternative hypothesis can be:\r\n\r\n<ul>\r\n\t<li>[latex] H_{A}: p&gt;\\text{null value}[\/latex],<\/li>\r\n\t<li>[latex] H_{A}: p&lt;\\text{null value}[\/latex], or<\/li>\r\n\t<li>[latex] H_{A}: p \\neq \\text{null value}[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox example\">A medical trial is conducted to test whether or not a new medicine reduces cholesterol by [latex]25\\%[\/latex]. State the null and alternative hypotheses.[reveal-answer q=\"114020\"]Show answer[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"114020\"][latex]H_0:[\/latex] The drug reduces cholesterol by [latex]25\\%[\/latex].That is: [latex]H_0: p = 0.25[\/latex][latex]H_{A}:[\/latex] The drug does not reduce cholesterol by [latex]25\\%[\/latex].\r\n\r\n<p>That is: [latex]H_{A}: p \\ne 0.25[\/latex]<\/p>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<p>[embed]https:\/\/www.youtube.com\/watch?v=5D1gV37bKXY[\/embed]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2809[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write a null and alternative hypothesis for a hypothesis test&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;}\">Write a null and alternative hypothesis for a hypothesis test.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Decide if a sample statistic provides enough evidence to reject the null hypothesis&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;}\">Decide if a sample statistic provides enough evidence to reject the null hypothesis.<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox recall\">The <strong>null hypothesis<\/strong>, [latex]H_{0}[\/latex], is what we assume to be true to begin with. This can often be considered the status quo, and as a result, if you cannot accept the null, it requires some action.<\/p>\n<ul>\n<li>For proportion, our parameter is population proportion, denoted [latex]p[\/latex], therefore our null hypothesis is [latex]H_0: p = \\text{null value}[\/latex]<\/li>\n<\/ul>\n<p>The <strong>alternative hypothesis<\/strong>, [latex]H_{A}[\/latex], is what we consider to be plausible if the null hypothesis is false. This is usually what the researcher is trying to prove.<\/p>\n<ul>\n<li>The alternative hypothesis can be:\n<ul>\n<li>[latex]H_{A}: p>\\text{null value}[\/latex],<\/li>\n<li>[latex]H_{A}: p<\\text{null value}[\/latex], or<\/li>\n<li>[latex]H_{A}: p \\neq \\text{null value}[\/latex].<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox example\">A medical trial is conducted to test whether or not a new medicine reduces cholesterol by [latex]25\\%[\/latex]. State the null and alternative hypotheses.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q114020\">Show answer<\/button><\/p>\n<div id=\"q114020\" class=\"hidden-answer\" style=\"display: none\">[latex]H_0:[\/latex] The drug reduces cholesterol by [latex]25\\%[\/latex].That is: [latex]H_0: p = 0.25[\/latex][latex]H_{A}:[\/latex] The drug does not reduce cholesterol by [latex]25\\%[\/latex].<\/p>\n<p>That is: [latex]H_{A}: p \\ne 0.25[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Simple hypothesis testing | Probability and Statistics | Khan Academy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/5D1gV37bKXY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2809\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2809&theme=lumen&iframe_resize_id=ohm2809&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":15,"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":"fresh_take","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\/1216"}],"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\/1216\/revisions"}],"predecessor-version":[{"id":6755,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1216\/revisions\/6755"}],"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\/1216\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1216"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1216"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1216"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}