{"id":1304,"date":"2023-06-22T02:13:33","date_gmt":"2023-06-22T02:13:33","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-difference-in-population-means-apply-it-1\/"},"modified":"2025-05-16T04:06:10","modified_gmt":"2025-05-16T04:06:10","slug":"confidence-interval-for-difference-in-population-means-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-difference-in-population-means-apply-it-1\/","title":{"raw":"Confidence Interval for Difference in Population Means: Apply It 1","rendered":"Confidence Interval for Difference in Population Means: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li class=\"li1\">Check the assumptions for a two-sample [latex]t[\/latex] confidence interval for population mean.<\/li>\r\n\t<li class=\"li1\">Calculate and explain a confidence interval for the difference between two population means.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox recall\">Confidence Interval:\u00a0<strong>estimate [latex]\\pm[\/latex] margin of error<\/strong><\/section>\r\n<h2>Cell Phones while Driving<\/h2>\r\n<p>Previously, we used data from a study investigating how driving while using a cell phone affects reaction time.[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. https:\/\/doi.org\/10.1111\/1467-9280.00386[\/footnote] In this study, [latex]64[\/latex] students were randomly assigned to one of two groups. Students in both groups were asked to drive in a driving simulator and to press a brake button as quickly as possible when they saw a red light. Response times (in milliseconds) were measured. Students in one group used their cell phones while driving in the simulator, and students in the other group did not use their cell phones.<\/p>\r\n<p>Let's use the data to estimate the difference between the mean reaction time for people who use their cell phones while driving and the mean reaction time for people who do not use their cell phones while driving.<\/p>\r\n<p>[reveal-answer q=\"777614\"]Steps[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"777614\"]<\/p>\r\n<p>Under the <strong>Confidence and Significance Tests<\/strong> tab:<\/p>\r\n<ul>\r\n\t<li>Select the <strong>Reaction Times<\/strong> data set.<\/li>\r\n\t<li>For <strong>Type of Inference<\/strong>, select <strong>Confidence Interval<\/strong>.<\/li>\r\n\t<li>Use the slider for the confidence level to select a 95% confidence level.[\/hidden-answer]<\/li>\r\n<\/ul>\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<div>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]1807[\/ohm2_question]<\/section>\r\n<\/div>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li class=\"li1\">Check the assumptions for a two-sample [latex]t[\/latex] confidence interval for population mean.<\/li>\n<li class=\"li1\">Calculate and explain a confidence interval for the difference between two population means.<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox recall\">Confidence Interval:\u00a0<strong>estimate [latex]\\pm[\/latex] margin of error<\/strong><\/section>\n<h2>Cell Phones while Driving<\/h2>\n<p>Previously, we used data from a study investigating how driving while using a cell phone affects reaction time.<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. https:\/\/doi.org\/10.1111\/1467-9280.00386\" id=\"return-footnote-1304-1\" href=\"#footnote-1304-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a> In this study, [latex]64[\/latex] students were randomly assigned to one of two groups. Students in both groups were asked to drive in a driving simulator and to press a brake button as quickly as possible when they saw a red light. Response times (in milliseconds) were measured. Students in one group used their cell phones while driving in the simulator, and students in the other group did not use their cell phones.<\/p>\n<p>Let&#8217;s use the data to estimate the difference between the mean reaction time for people who use their cell phones while driving and the mean reaction time for people who do not use their cell phones while driving.<\/p>\n<p><div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q777614\">Steps<\/button><\/p>\n<div id=\"q777614\" class=\"hidden-answer\" style=\"display: none\">\n<p>Under the <strong>Confidence and Significance Tests<\/strong> tab:<\/p>\n<ul>\n<li>Select the <strong>Reaction Times<\/strong> data set.<\/li>\n<li>For <strong>Type of Inference<\/strong>, select <strong>Confidence Interval<\/strong>.<\/li>\n<li>Use the slider for the confidence level to select a 95% confidence level.<\/div>\n<\/div>\n<\/li>\n<\/ul>\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<div>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm1807\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1807&theme=lumen&iframe_resize_id=ohm1807&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/div>\n<hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1304-1\">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. https:\/\/doi.org\/10.1111\/1467-9280.00386 <a href=\"#return-footnote-1304-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":8,"menu_order":32,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1268,"module-header":"apply_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\/1304"}],"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":4,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1304\/revisions"}],"predecessor-version":[{"id":6799,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1304\/revisions\/6799"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1268"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1304\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1304"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1304"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1304"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}