{"id":1320,"date":"2023-06-22T02:17:30","date_gmt":"2023-06-22T02:17:30","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypothesis-for-means-dig-deeper\/"},"modified":"2025-05-16T22:19:54","modified_gmt":"2025-05-16T22:19:54","slug":"null-and-alternative-hypothesis-for-means-dig-deeper","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypothesis-for-means-dig-deeper\/","title":{"raw":"Null and Alternative Hypothesis for Means: Fresh Take","rendered":"Null and Alternative Hypothesis for Means: 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;Explain the purpose of hypothesis testing&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;}\">Explain the purpose of hypothesis testing.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write the null and alternative hypotheses for tests on population means&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 the null and alternative hypotheses for tests on population means.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions for hypothesis tests for population means&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;}\">Check the conditions for hypothesis tests for population means.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox recall\">The <strong>null hypothesis ([latex]H_0[\/latex])<\/strong> is a statement of no change or status quo.\u00a0Symbol used for the null hypothesis is [latex]=[\/latex].\r\n\r\n<p>The <strong>alternative hypothesis ([latex]H_A[\/latex])<\/strong> is sometimes referred to as the research hypothesis; it is what the researcher believes to be true based on the data to be collected. Symbols used for the alternative hypothesis are [latex]\\lt[\/latex], [latex]\\gt[\/latex], and [latex]\\ne[\/latex].<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">We want to test whether the mean GPA of students in American colleges is different from 2.0. The null and alternative hypotheses are:\r\n\r\n<p>[latex]H_0: \\mu=2.0[\/latex][latex]H_A: \\mu \\ne 2.0[\/latex]<\/p>\r\n<p>Note: Because we are testing [latex]\\ne[\/latex], this is a two-tailed test.<\/p>\r\n<\/section>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<p>[embed]https:\/\/youtu.be\/89Dp9Xq4eaA[\/embed]<\/p>\r\n<p>[embed]https:\/\/youtu.be\/GtokpL4f32s[\/embed]<\/p>\r\n<\/section>\r\n<p>&nbsp;<\/p>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Explain the purpose of hypothesis testing&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;}\">Explain the purpose of hypothesis testing.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Write the null and alternative hypotheses for tests on population means&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 the null and alternative hypotheses for tests on population means.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Check the conditions for hypothesis tests for population means&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;}\">Check the conditions for hypothesis tests for population means.<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox recall\">The <strong>null hypothesis ([latex]H_0[\/latex])<\/strong> is a statement of no change or status quo.\u00a0Symbol used for the null hypothesis is [latex]=[\/latex].<\/p>\n<p>The <strong>alternative hypothesis ([latex]H_A[\/latex])<\/strong> is sometimes referred to as the research hypothesis; it is what the researcher believes to be true based on the data to be collected. Symbols used for the alternative hypothesis are [latex]\\lt[\/latex], [latex]\\gt[\/latex], and [latex]\\ne[\/latex].<\/p>\n<\/section>\n<section class=\"textbox example\">We want to test whether the mean GPA of students in American colleges is different from 2.0. The null and alternative hypotheses are:<\/p>\n<p>[latex]H_0: \\mu=2.0[\/latex][latex]H_A: \\mu \\ne 2.0[\/latex]<\/p>\n<p>Note: Because we are testing [latex]\\ne[\/latex], this is a two-tailed test.<\/p>\n<\/section>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Writing hypotheses for a significance test about a mean | AP Statistics | Khan Academy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/89Dp9Xq4eaA?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Conditions for a t test about a mean | AP Statistics | Khan Academy\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/GtokpL4f32s?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/section>\n<p>&nbsp;<\/p>\n","protected":false},"author":8,"menu_order":13,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1309,"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\/1320"}],"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":4,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1320\/revisions"}],"predecessor-version":[{"id":6806,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1320\/revisions\/6806"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1309"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1320\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1320"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1320"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1320"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1320"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}