{"id":2376,"date":"2023-08-03T22:41:42","date_gmt":"2023-08-03T22:41:42","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/?post_type=chapter&#038;p=2376"},"modified":"2024-04-30T15:53:13","modified_gmt":"2024-04-30T15:53:13","slug":"null-and-alternative-hypothesis-for-means-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/null-and-alternative-hypothesis-for-means-learn-it-3\/","title":{"raw":"Null and Alternative Hypothesis for Means: Learn It 3","rendered":"Null and Alternative Hypothesis for Means: Learn It 3"},"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>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3><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;}\">null and alternative hypotheses<\/span><\/h3>\r\n<p>The<strong> null hypothesis ([latex]H_0[\/latex]) <\/strong>is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.<\/p>\r\n<ul>\r\n\t<li>One-sample null hypothesis: [latex]H_0: \\mu=\\mu_0[\/latex], [latex]\\mu_0[\/latex] is the null value.<\/li>\r\n\t<li>Two-sample null hypothesis: [latex]H_0: \\mu_1=\\mu_2[\/latex] or [latex]H_0: \\mu_1-\\mu_2=0[\/latex]<\/li>\r\n<\/ul>\r\n<p>The<strong> alternative hypothesis ([latex]H_A[\/latex])<\/strong>\u00a0is a claim about the population that is contradictory to [latex]H_0[\/latex] and what we conclude when we reject [latex]H_0[\/latex].<\/p>\r\n<ul>\r\n\t<li>One-sample alternative hypothesis:\r\n\r\n<ul>\r\n\t<li>[latex]H_A: \\mu \\lt \\mu_0[\/latex], [latex]\\mu_0[\/latex] is the null value.<\/li>\r\n\t<li>[latex]H_A: \\mu&gt;\\mu_0[\/latex], [latex]\\mu_0[\/latex] is the null value.<\/li>\r\n\t<li>[latex]H_A: \\mu\\ne \\mu_0[\/latex], [latex]\\mu_0[\/latex] is the null value.<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t<li>Two-sample alternative hypothesis:\r\n\r\n<ul>\r\n\t<li>[latex]H_A: \\mu_1\\lt \\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2\\lt 0[\/latex]<\/li>\r\n\t<li>[latex]H_A: \\mu_1&gt;\\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2&gt;0[\/latex]<\/li>\r\n\t<li>[latex]H_A: \\mu_1\\ne \\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2\\ne0[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<p>Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.<\/p>\r\n<\/section>\r\n<p>The data set can be accessed here: <a href=\"https:\/\/docs.google.com\/spreadsheets\/d\/15RIs8K9MaGVfYQmi15bH87dUIz8X1o60WcsukoLlFFo\/edit?usp=sharing\">Coca-Cola Data Set<\/a>.<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1401[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1402[\/ohm2_question]<\/section>","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>\n<section class=\"textbox keyTakeaway\">\n<h3><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;}\">null and alternative hypotheses<\/span><\/h3>\n<p>The<strong> null hypothesis ([latex]H_0[\/latex]) <\/strong>is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.<\/p>\n<ul>\n<li>One-sample null hypothesis: [latex]H_0: \\mu=\\mu_0[\/latex], [latex]\\mu_0[\/latex] is the null value.<\/li>\n<li>Two-sample null hypothesis: [latex]H_0: \\mu_1=\\mu_2[\/latex] or [latex]H_0: \\mu_1-\\mu_2=0[\/latex]<\/li>\n<\/ul>\n<p>The<strong> alternative hypothesis ([latex]H_A[\/latex])<\/strong>\u00a0is a claim about the population that is contradictory to [latex]H_0[\/latex] and what we conclude when we reject [latex]H_0[\/latex].<\/p>\n<ul>\n<li>One-sample alternative hypothesis:\n<ul>\n<li>[latex]H_A: \\mu \\lt \\mu_0[\/latex], [latex]\\mu_0[\/latex] is the null value.<\/li>\n<li>[latex]H_A: \\mu>\\mu_0[\/latex], [latex]\\mu_0[\/latex] is the null value.<\/li>\n<li>[latex]H_A: \\mu\\ne \\mu_0[\/latex], [latex]\\mu_0[\/latex] is the null value.<\/li>\n<\/ul>\n<\/li>\n<li>Two-sample alternative hypothesis:\n<ul>\n<li>[latex]H_A: \\mu_1\\lt \\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2\\lt 0[\/latex]<\/li>\n<li>[latex]H_A: \\mu_1>\\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2>0[\/latex]<\/li>\n<li>[latex]H_A: \\mu_1\\ne \\mu_2[\/latex] or [latex]H_A: \\mu_1-\\mu_2\\ne0[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.<\/p>\n<\/section>\n<p>The data set can be accessed here: <a href=\"https:\/\/docs.google.com\/spreadsheets\/d\/15RIs8K9MaGVfYQmi15bH87dUIz8X1o60WcsukoLlFFo\/edit?usp=sharing\">Coca-Cola Data Set<\/a>.<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1401\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1401&theme=lumen&iframe_resize_id=ohm1401&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1402\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1402&theme=lumen&iframe_resize_id=ohm1402&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":9,"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":"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\/2376"}],"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\/12"}],"version-history":[{"count":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2376\/revisions"}],"predecessor-version":[{"id":6009,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/2376\/revisions\/6009"}],"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\/2376\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=2376"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=2376"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=2376"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=2376"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}