{"id":1323,"date":"2023-06-22T02:17:33","date_gmt":"2023-06-22T02:17:33","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/one-sample-hypothesis-test-for-means-apply-it-1\/"},"modified":"2025-05-16T22:21:20","modified_gmt":"2025-05-16T22:21:20","slug":"one-sample-hypothesis-test-for-means-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/one-sample-hypothesis-test-for-means-apply-it-1\/","title":{"raw":"One-Sample Hypothesis Test for Means: Learn It 1","rendered":"One-Sample Hypothesis Test for Means: Learn It 1"},"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<p>In this section, we will learn to conduct a hypothesis test about a population mean and state a conclusion in context under appropriate conditions.<\/p>\r\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\r\n<p>[embed]https:\/\/www.youtube.com\/watch?v=i26jwq7d5C0[\/embed]<\/p>\r\n<p>&nbsp;<\/p>\r\n<\/section>\r\n<p>We did hypothesis tests previously. The steps and logic in conducting a hypothesis test about a population mean are the same as the a hypothesis test involving population proportions.<\/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<h3>Plastics Pollution<\/h3>\r\n<p><img class=\"aligncenter wp-image-810 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211711\/Picture1-9.jpg\" alt=\"Plastic waste surrounding a globe.\" width=\"300\" height=\"199\" \/><\/p>\r\n<p>Plastic pollution has become one of the most\u00a0pressing environmental issues, as rapidly increasing production of disposable plastic products overwhelms the world\u2019s ability to deal with them.[footnote]https:\/\/www.nationalgeographic.com\/environment\/article\/plastic-pollution[\/footnote] The United States welcomes the historic opportunity at the United Nations Environment Assembly (UNEA 5.2), February-March 2022, to start a process with other nations and stakeholders to fight plastic pollution. The United States is already acting both domestically and internationally to address this global challenge.[footnote]https:\/\/www.state.gov\/u-s-actions-to-address-plastic-pollution\/[\/footnote]<\/p>\r\n<p>What about us? Are you aware of how much plastic we are using in our lives?<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]857[\/ohm2_question]<\/section>\r\n<p>Before we get into the details, let\u2019s practice identifying research questions, writing the hypotheses accordingly, and knowing the steps in conducting a hypothesis test that involves a population mean.<\/p>\r\n<section class=\"textbox recall\">\r\n<ul>\r\n\t<li>Notation for\u00a0<strong>population<\/strong> mean: [latex]\\mu[\/latex] (pronounce as \"mu\")<\/li>\r\n\t<li>Notation for\u00a0<strong>sample<\/strong> mean: [latex]\\bar{x}[\/latex] (pronounce as \"x-bar\")<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]11103[\/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<p>In this section, we will learn to conduct a hypothesis test about a population mean and state a conclusion in context under appropriate conditions.<\/p>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Why All the Likes\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/i26jwq7d5C0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<\/section>\n<p>We did hypothesis tests previously. The steps and logic in conducting a hypothesis test about a population mean are the same as the a hypothesis test involving population proportions.<\/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<h3>Plastics Pollution<\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-810 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211711\/Picture1-9.jpg\" alt=\"Plastic waste surrounding a globe.\" width=\"300\" height=\"199\" \/><\/p>\n<p>Plastic pollution has become one of the most\u00a0pressing environmental issues, as rapidly increasing production of disposable plastic products overwhelms the world\u2019s ability to deal with them.<a class=\"footnote\" title=\"https:\/\/www.nationalgeographic.com\/environment\/article\/plastic-pollution\" id=\"return-footnote-1323-1\" href=\"#footnote-1323-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> The United States welcomes the historic opportunity at the United Nations Environment Assembly (UNEA 5.2), February-March 2022, to start a process with other nations and stakeholders to fight plastic pollution. The United States is already acting both domestically and internationally to address this global challenge.<a class=\"footnote\" title=\"https:\/\/www.state.gov\/u-s-actions-to-address-plastic-pollution\/\" id=\"return-footnote-1323-2\" href=\"#footnote-1323-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<p>What about us? Are you aware of how much plastic we are using in our lives?<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm857\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=857&theme=lumen&iframe_resize_id=ohm857&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Before we get into the details, let\u2019s practice identifying research questions, writing the hypotheses accordingly, and knowing the steps in conducting a hypothesis test that involves a population mean.<\/p>\n<section class=\"textbox recall\">\n<ul>\n<li>Notation for\u00a0<strong>population<\/strong> mean: [latex]\\mu[\/latex] (pronounce as &#8220;mu&#8221;)<\/li>\n<li>Notation for\u00a0<strong>sample<\/strong> mean: [latex]\\bar{x}[\/latex] (pronounce as &#8220;x-bar&#8221;)<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm11103\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=11103&theme=lumen&iframe_resize_id=ohm11103&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1323-1\">https:\/\/www.nationalgeographic.com\/environment\/article\/plastic-pollution <a href=\"#return-footnote-1323-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-1323-2\">https:\/\/www.state.gov\/u-s-actions-to-address-plastic-pollution\/ <a href=\"#return-footnote-1323-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":14,"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\/1323"}],"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":11,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1323\/revisions"}],"predecessor-version":[{"id":6808,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1323\/revisions\/6808"}],"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\/1323\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1323"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1323"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1323"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}