{"id":1344,"date":"2023-06-22T02:17:51","date_gmt":"2023-06-22T02:17:51","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-two-population-means-dependent-samples-apply-it-5\/"},"modified":"2025-05-16T22:43:00","modified_gmt":"2025-05-16T22:43:00","slug":"comparing-two-population-means-dependent-samples-apply-it-5","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/comparing-two-population-means-dependent-samples-apply-it-5\/","title":{"raw":"Comparing Two Population Means (Dependent Samples): Learn It 5","rendered":"Comparing Two Population Means (Dependent Samples): Learn It 5"},"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;Describe how a two-sample confidence interval is related to a hypothesis test for the difference between two dependent 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;}\">Describe how a two-sample confidence interval is related to a hypothesis test for the difference between two dependent population means<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Inferences with Confidence Intervals<\/h2>\r\n<p>A confidence interval provides a range of population values with which a sample statistic is consistent at a given confidence level. In many cases, confidence intervals can also be used to either reject or not reject the null hypothesis, and therefore perform the same function as the typical hypothesis test. A [latex]95\\%[\/latex] confidence interval would be used to test the null hypothesis at the [latex]5\\%[\/latex] significance level. A [latex]99\\%[\/latex] confidence interval would be used to test the null hypothesis at the [latex]1\\%[\/latex] significance level.<\/p>\r\n<p>Let's find the [latex]95\\%[\/latex] confidence interval and see if we can answer the research question: \u201cDoes a driver\u2019s reaction times (in milliseconds) differ when they are using a cell phone as opposed to when they are not using a cell phone?\u201d<\/p>\r\n<section class=\"textbox interact\">Use the following steps:\r\n\r\n<p style=\"padding-left: 40px;\"><strong>Step 1: <\/strong>Click on the tab <strong>Two Dependent Samples<\/strong>.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 2: <\/strong>In the \u201cDataset\u201d drop-down menu, choose \u201cReaction Times (Paired Experiment).\u201d<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 3: <\/strong>In the left column, go to the drop-down menu for \u201cType of Inference\u201d and select \u201cConfidence Interval\u201d.<\/p>\r\n<p style=\"padding-left: 40px;\"><strong>Step 4: <\/strong>Use the slider to select the correct \"Confidence Level\".<\/p>\r\n<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/2samplemean\/ \" width=\"100%\" height=\"1150\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\"><\/span><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/2samplemean\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]895[\/ohm2_question]<\/section>\r\n<section>\r\n<section class=\"textbox recall\">\r\n<ul>\r\n\t<li>If a confidence interval contains the hypothesized parameter, a hypothesis test at the [latex]0.05[\/latex] level will\u00a0<em>almost always<\/em>\u00a0fail to reject the null hypothesis.<\/li>\r\n\t<li>If the [latex]95\\%[\/latex] confidence interval does not contain the hypothesized parameter, a hypothesis test at the [latex]0.05[\/latex] level will\u00a0<em>almost always<\/em>\u00a0reject the null hypothesis.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Describe how a two-sample confidence interval is related to a hypothesis test for the difference between two dependent 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;}\">Describe how a two-sample confidence interval is related to a hypothesis test for the difference between two dependent population means<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Inferences with Confidence Intervals<\/h2>\n<p>A confidence interval provides a range of population values with which a sample statistic is consistent at a given confidence level. In many cases, confidence intervals can also be used to either reject or not reject the null hypothesis, and therefore perform the same function as the typical hypothesis test. A [latex]95\\%[\/latex] confidence interval would be used to test the null hypothesis at the [latex]5\\%[\/latex] significance level. A [latex]99\\%[\/latex] confidence interval would be used to test the null hypothesis at the [latex]1\\%[\/latex] significance level.<\/p>\n<p>Let&#8217;s find the [latex]95\\%[\/latex] confidence interval and see if we can answer the research question: \u201cDoes a driver\u2019s reaction times (in milliseconds) differ when they are using a cell phone as opposed to when they are not using a cell phone?\u201d<\/p>\n<section class=\"textbox interact\">Use the following steps:<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 1: <\/strong>Click on the tab <strong>Two Dependent Samples<\/strong>.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 2: <\/strong>In the \u201cDataset\u201d drop-down menu, choose \u201cReaction Times (Paired Experiment).\u201d<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 3: <\/strong>In the left column, go to the drop-down menu for \u201cType of Inference\u201d and select \u201cConfidence Interval\u201d.<\/p>\n<p style=\"padding-left: 40px;\"><strong>Step 4: <\/strong>Use the slider to select the correct &#8220;Confidence Level&#8221;.<\/p>\n<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/2samplemean\/\" width=\"100%\" height=\"1150\" frameborder=\"no\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\"><\/span><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/2samplemean\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm895\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=895&theme=lumen&iframe_resize_id=ohm895&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<section class=\"textbox recall\">\n<ul>\n<li>If a confidence interval contains the hypothesized parameter, a hypothesis test at the [latex]0.05[\/latex] level will\u00a0<em>almost always<\/em>\u00a0fail to reject the null hypothesis.<\/li>\n<li>If the [latex]95\\%[\/latex] confidence interval does not contain the hypothesized parameter, a hypothesis test at the [latex]0.05[\/latex] level will\u00a0<em>almost always<\/em>\u00a0reject the null hypothesis.<\/li>\n<\/ul>\n<\/section>\n<\/section>\n","protected":false},"author":8,"menu_order":30,"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\/1344"}],"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":7,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1344\/revisions"}],"predecessor-version":[{"id":6826,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1344\/revisions\/6826"}],"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\/1344\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1344"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1344"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1344"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1344"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}