{"id":1340,"date":"2023-06-22T02:17:47","date_gmt":"2023-06-22T02:17:47","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-two-population-means-dependent-samples-apply-it-1\/"},"modified":"2025-05-16T22:40:09","modified_gmt":"2025-05-16T22:40:09","slug":"comparing-two-population-means-dependent-samples-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-two-population-means-dependent-samples-apply-it-1\/","title":{"raw":"Comparing Two Population Means (Dependent Samples): Learn It 1","rendered":"Comparing Two Population Means (Dependent Samples): 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 two-sample t-test for dependent population 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 two-sample [latex]t[\/latex]-test for dependent population means from hypotheses to conclusions<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Dependent Samples vs. Independent Samples<\/h2>\r\n<p>Previously, you learned how to create confidence intervals and conduct hypothesis tests with a single variable. You also learned how to compare means or proportions from two samples. Some statistical studies use samples from more than one population. In order to compare the difference between two populations, it is important to identify if the samples are dependent (paired) or independent. Dependent and independent sample hypothesis tests are used to answer questions about the difference between two population means.<\/p>\r\n<section class=\"textbox recall\">For <strong>dependent (paired) samples<\/strong>, the same variable is recorded for each sample, and there is a logical way to pair the observations from one sample with the observations in the other sample.\r\n\r\n<p>In contrast, when samples are <strong>independently<\/strong> selected, the same variable is measured for both samples, but there is no logical way to pair an observation from one sample with a particular observation from the other sample.<\/p>\r\n<\/section>\r\n<h4>Do not use your cell phone while driving!<\/h4>\r\n<p><img class=\"aligncenter wp-image-881 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211721\/Picture1-10.jpg\" alt=\"A person looking at their phone while driving.\" width=\"300\" height=\"201\" \/><\/p>\r\n<p>The study in this in-class activity uses a single group of participants and measures their reaction times (in milliseconds) while performing a driving task without using their cell phones and then again while using their cell phones.[footnote]Strayer, D. L. &amp; Johnston, W. A. (2001, November 1). Driven to distraction: Dual-task studies of simulated driving and conversing on a cellular telephone. Psychological Science, 12(6), 462\u2013466. DOI: 10.1111\/1467-9280.00386[\/footnote]<\/p>\r\n<div>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]891[\/ohm2_question]<\/section>\r\n<p>The data collected include the reaction times (in milliseconds) with and without the use of cell phones for [latex]32[\/latex] randomly selected participants. Therefore, each participant will have two reaction times, one for using a cell phone while driving and another for not using a cell phone while driving.<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]892[\/ohm2_question]<\/section>\r\n<\/div>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Complete a two-sample t-test for dependent population 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 two-sample [latex]t[\/latex]-test for dependent population means from hypotheses to conclusions<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Dependent Samples vs. Independent Samples<\/h2>\n<p>Previously, you learned how to create confidence intervals and conduct hypothesis tests with a single variable. You also learned how to compare means or proportions from two samples. Some statistical studies use samples from more than one population. In order to compare the difference between two populations, it is important to identify if the samples are dependent (paired) or independent. Dependent and independent sample hypothesis tests are used to answer questions about the difference between two population means.<\/p>\n<section class=\"textbox recall\">For <strong>dependent (paired) samples<\/strong>, the same variable is recorded for each sample, and there is a logical way to pair the observations from one sample with the observations in the other sample.<\/p>\n<p>In contrast, when samples are <strong>independently<\/strong> selected, the same variable is measured for both samples, but there is no logical way to pair an observation from one sample with a particular observation from the other sample.<\/p>\n<\/section>\n<h4>Do not use your cell phone while driving!<\/h4>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-881 size-medium\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/10\/2022\/11\/23211721\/Picture1-10.jpg\" alt=\"A person looking at their phone while driving.\" width=\"300\" height=\"201\" \/><\/p>\n<p>The study in this in-class activity uses a single group of participants and measures their reaction times (in milliseconds) while performing a driving task without using their cell phones and then again while using their cell phones.<a class=\"footnote\" title=\"Strayer, D. L. &amp; Johnston, W. A. (2001, November 1). Driven to distraction: Dual-task studies of simulated driving and conversing on a cellular telephone. Psychological Science, 12(6), 462\u2013466. DOI: 10.1111\/1467-9280.00386\" id=\"return-footnote-1340-1\" href=\"#footnote-1340-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm891\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=891&theme=lumen&iframe_resize_id=ohm891&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>The data collected include the reaction times (in milliseconds) with and without the use of cell phones for [latex]32[\/latex] randomly selected participants. Therefore, each participant will have two reaction times, one for using a cell phone while driving and another for not using a cell phone while driving.<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm892\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=892&theme=lumen&iframe_resize_id=ohm892&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1340-1\">Strayer, D. L. &amp; Johnston, W. A. (2001, November 1). Driven to distraction: Dual-task studies of simulated driving and conversing on a cellular telephone. Psychological Science, 12(6), 462\u2013466. DOI: 10.1111\/1467-9280.00386 <a href=\"#return-footnote-1340-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":26,"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\/1340"}],"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":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1340\/revisions"}],"predecessor-version":[{"id":6822,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1340\/revisions\/6822"}],"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\/1340\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1340"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1340"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1340"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1340"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}