{"id":1505,"date":"2023-06-22T02:40:11","date_gmt":"2023-06-22T02:40:11","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/module-18-background-youll-need-2\/"},"modified":"2025-05-17T02:48:21","modified_gmt":"2025-05-17T02:48:21","slug":"module-18-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/module-18-background-youll-need-2\/","title":{"raw":"Module 17: Background You'll Need 2","rendered":"Module 17: Background You&#8217;ll Need 2"},"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;Calculate confidence intervals for a population mean using the t Distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12928,&quot;10&quot;:2,&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Calculate confidence intervals for a population mean using the [latex]t[\/latex] Distribution<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2><strong>The [latex]t[\/latex] Confidence Interval for a Population Mean<\/strong><\/h2>\r\n<section class=\"textbox recall\">The conditions for the one-sample [latex]t[\/latex] confidence interval are:\r\n\r\n<ul>\r\n\t<li>The sample is a random sample from the population of interest.<\/li>\r\n\t<li>The sample size is at least [latex]30[\/latex] or the population distribution is approximately normal.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Choose the \u201cCell Phone Reaction Times\u201d data set from the dropdown menu.<br \/>\r\nThe data set consists of differences in reaction times (in milliseconds) recorded for a sample of people both when they were using cell phones and when they were not using cell phones.<br \/>\r\n<strong>Step 2: <\/strong>For \u201cType of Inference,\u201d select \u201cConfidence Interval\u201d and set the confidence level to 95%.<br \/>\r\nMake sure that \u201cInterval\u201d is selected where it asks \u201cInterval, Lower or Upper Bound?\u201d<\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/inference_mean\/\" width=\"100%\" height=\"1050\" frameborder=\"no\"><\/iframe><br \/>\r\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/inference_mean\/\" 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]3477[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3478[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3479[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3480[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate confidence intervals for a population mean using the t Distribution&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12928,&quot;10&quot;:2,&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Calculate confidence intervals for a population mean using the [latex]t[\/latex] Distribution<\/span><\/li>\n<\/ul>\n<\/section>\n<h2><strong>The [latex]t[\/latex] Confidence Interval for a Population Mean<\/strong><\/h2>\n<section class=\"textbox recall\">The conditions for the one-sample [latex]t[\/latex] confidence interval are:<\/p>\n<ul>\n<li>The sample is a random sample from the population of interest.<\/li>\n<li>The sample size is at least [latex]30[\/latex] or the population distribution is approximately normal.<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Choose the \u201cCell Phone Reaction Times\u201d data set from the dropdown menu.<br \/>\nThe data set consists of differences in reaction times (in milliseconds) recorded for a sample of people both when they were using cell phones and when they were not using cell phones.<br \/>\n<strong>Step 2: <\/strong>For \u201cType of Inference,\u201d select \u201cConfidence Interval\u201d and set the confidence level to 95%.<br \/>\nMake sure that \u201cInterval\u201d is selected where it asks \u201cInterval, Lower or Upper Bound?\u201d<\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/inference_mean\/\" width=\"100%\" height=\"1050\" frameborder=\"no\"><\/iframe><br \/>\n[<a href=\"https:\/\/lumen-learning.shinyapps.io\/inference_mean\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3477\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3477&theme=lumen&iframe_resize_id=ohm3477&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3478\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3478&theme=lumen&iframe_resize_id=ohm3478&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3479\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3479&theme=lumen&iframe_resize_id=ohm3479&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3480\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3480&theme=lumen&iframe_resize_id=ohm3480&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":1502,"module-header":"background_you_need","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\/1505"}],"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\/1505\/revisions"}],"predecessor-version":[{"id":6917,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1505\/revisions\/6917"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1502"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1505\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1505"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1505"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1505"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}