{"id":1294,"date":"2023-06-22T02:13:24","date_gmt":"2023-06-22T02:13:24","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-a-population-mean-learn-it-3\/"},"modified":"2025-05-16T04:02:19","modified_gmt":"2025-05-16T04:02:19","slug":"confidence-interval-for-a-population-mean-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/confidence-interval-for-a-population-mean-learn-it-3\/","title":{"raw":"Confidence Interval for a Population Mean: Learn It 3","rendered":"Confidence Interval for a Population Mean: Learn It 3"},"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;Check the assumptions for a one-sample t confidence interval for population mean&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4865,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:3,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Check the assumptions for a one-sample [latex]t[\/latex] confidence interval for population mean.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate a confidence interval for a population mean and explain what it means&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4865,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:3,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate a confidence interval for a population mean and explain what it means.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<section>\r\n<h2>Making Inferences about a Population Mean<\/h2>\r\n<p>As was the case with previous inference methods, there are a few assumptions\/conditions that you should check before using the one-sample [latex]t[\/latex]-interval. Two important ones are:<\/p>\r\n<ul>\r\n\t<li>The sample is a random sample from the population of interest, or it is reasonable to regard the sample as if it were a random sample. It is reasonable to regard the sample as a random sample if it was selected in a way that should result in a sample that is representative of the population.<\/li>\r\n\t<li>The population distribution of the variable that was measured is approximately normal, or the sample size is large. Usually, a sample of size [latex]30[\/latex] or more is considered to be \u201clarge.\u201d If the sample size is less than [latex]30[\/latex], you should look at a plot of the data (a dotplot, a boxplot, or, if the sample size isn\u2019t really small, a histogram) to make sure that the distribution looks approximately symmetric and that there are no outliers.<\/li>\r\n<\/ul>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/inference_mean\/ \" width=\"100%\" height=\"1075\" 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\/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]1803[\/ohm2_question]<\/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;Check the assumptions for a one-sample t confidence interval for population mean&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4865,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:3,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Check the assumptions for a one-sample [latex]t[\/latex] confidence interval for population mean.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Calculate a confidence interval for a population mean and explain what it means&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:4865,&quot;3&quot;:{&quot;1&quot;:0},&quot;11&quot;:3,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;}\">Calculate a confidence interval for a population mean and explain what it means.<\/span><\/li>\n<\/ul>\n<\/section>\n<section>\n<h2>Making Inferences about a Population Mean<\/h2>\n<p>As was the case with previous inference methods, there are a few assumptions\/conditions that you should check before using the one-sample [latex]t[\/latex]-interval. Two important ones are:<\/p>\n<ul>\n<li>The sample is a random sample from the population of interest, or it is reasonable to regard the sample as if it were a random sample. It is reasonable to regard the sample as a random sample if it was selected in a way that should result in a sample that is representative of the population.<\/li>\n<li>The population distribution of the variable that was measured is approximately normal, or the sample size is large. Usually, a sample of size [latex]30[\/latex] or more is considered to be \u201clarge.\u201d If the sample size is less than [latex]30[\/latex], you should look at a plot of the data (a dotplot, a boxplot, or, if the sample size isn\u2019t really small, a histogram) to make sure that the distribution looks approximately symmetric and that there are no outliers.<\/li>\n<\/ul>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/inference_mean\/\" width=\"100%\" height=\"1075\" 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\/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=\"ohm1803\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1803&theme=lumen&iframe_resize_id=ohm1803&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<\/section>\n","protected":false},"author":8,"menu_order":23,"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":"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\/1294"}],"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\/1294\/revisions"}],"predecessor-version":[{"id":6793,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1294\/revisions\/6793"}],"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\/1294\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1294"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1294"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1294"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1294"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}