{"id":1326,"date":"2023-06-22T02:17:35","date_gmt":"2023-06-22T02:17:35","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/one-sample-hypothesis-test-for-means-dig-deeper\/"},"modified":"2025-05-16T22:27:05","modified_gmt":"2025-05-16T22:27:05","slug":"one-sample-hypothesis-test-for-means-dig-deeper","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/one-sample-hypothesis-test-for-means-dig-deeper\/","title":{"raw":"One-Sample Hypothesis Test for Means: Fresh Take","rendered":"One-Sample Hypothesis Test 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;Complete a one-sample t-test for means from hypotheses to conclusions&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;}\">Complete a one-sample [latex]t[\/latex]-test for means from hypotheses to conclusions.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2><strong>Hypothesis Testing about Weekly Work Hours<\/strong><\/h2>\r\n<p>Let's review the steps for hypothesis testing and see if we would be able to apply them to a one-sample hypothesis test for means (one-sample [latex]t[\/latex]-test).<\/p>\r\n<section class=\"textbox recall\"><strong>Steps for Hypothesis Testing<\/strong>\r\n<ol>\r\n\t<li>Write out the null and alternative hypotheses.<\/li>\r\n\t<li>Check the conditions for the hypothesis test.<\/li>\r\n\t<li>Calculate a test statistic.<\/li>\r\n\t<li>Calculate a P-value.<\/li>\r\n\t<li>Compare the P-value to the significance level, [latex]\\alpha[\/latex], to make a decision.<br \/>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>Decision<\/strong><\/td>\r\n<td><strong>Conclusion<\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>If P-value [latex]\\le\\alpha[\/latex], there is enough evidence to reject the null hypothesis.<\/td>\r\n<td>At the [latex]\\alpha\\times[\/latex]100% significance level, the data provide convincing evidence in support of the alternative hypothesis.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>If P-value [latex]\\gt\\alpha[\/latex], there is not enough evidence to reject the null hypothesis.<\/td>\r\n<td>At the [latex]\\alpha\\times[\/latex]100% significance level, the data do not provide convincing evidence in support of the alternative hypothesis.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n\t<li>Write a conclusion in context (e.g., we do\/do not have convincing evidence\u2026).<\/li>\r\n<\/ol>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1404[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]992[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]845[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]849[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]855[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]860[\/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 one-sample t-test for means from hypotheses to conclusions&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;}\">Complete a one-sample [latex]t[\/latex]-test for means from hypotheses to conclusions.<\/span><\/li>\n<\/ul>\n<\/section>\n<h2><strong>Hypothesis Testing about Weekly Work Hours<\/strong><\/h2>\n<p>Let&#8217;s review the steps for hypothesis testing and see if we would be able to apply them to a one-sample hypothesis test for means (one-sample [latex]t[\/latex]-test).<\/p>\n<section class=\"textbox recall\"><strong>Steps for Hypothesis Testing<\/strong><\/p>\n<ol>\n<li>Write out the null and alternative hypotheses.<\/li>\n<li>Check the conditions for the hypothesis test.<\/li>\n<li>Calculate a test statistic.<\/li>\n<li>Calculate a P-value.<\/li>\n<li>Compare the P-value to the significance level, [latex]\\alpha[\/latex], to make a decision.<br \/>\n<table>\n<tbody>\n<tr>\n<td><strong>Decision<\/strong><\/td>\n<td><strong>Conclusion<\/strong><\/td>\n<\/tr>\n<tr>\n<td>If P-value [latex]\\le\\alpha[\/latex], there is enough evidence to reject the null hypothesis.<\/td>\n<td>At the [latex]\\alpha\\times[\/latex]100% significance level, the data provide convincing evidence in support of the alternative hypothesis.<\/td>\n<\/tr>\n<tr>\n<td>If P-value [latex]\\gt\\alpha[\/latex], there is not enough evidence to reject the null hypothesis.<\/td>\n<td>At the [latex]\\alpha\\times[\/latex]100% significance level, the data do not provide convincing evidence in support of the alternative hypothesis.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Write a conclusion in context (e.g., we do\/do not have convincing evidence\u2026).<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1404\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1404&theme=lumen&iframe_resize_id=ohm1404&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm992\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=992&theme=lumen&iframe_resize_id=ohm992&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm845\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=845&theme=lumen&iframe_resize_id=ohm845&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm849\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=849&theme=lumen&iframe_resize_id=ohm849&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm855\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=855&theme=lumen&iframe_resize_id=ohm855&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm860\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=860&theme=lumen&iframe_resize_id=ohm860&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":19,"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\/1326"}],"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":6,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1326\/revisions"}],"predecessor-version":[{"id":6813,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1326\/revisions\/6813"}],"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\/1326\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1326"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1326"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1326"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}