{"id":1274,"date":"2023-06-22T02:13:08","date_gmt":"2023-06-22T02:13:08","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sampling-distribution-of-a-sample-mean-learn-it-2\/"},"modified":"2025-05-16T03:56:30","modified_gmt":"2025-05-16T03:56:30","slug":"sampling-distribution-of-a-sample-mean-learn-it-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sampling-distribution-of-a-sample-mean-learn-it-2\/","title":{"raw":"Sampling Distribution of a Sample Mean: Apply It 1","rendered":"Sampling Distribution of a Sample Mean: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Create a sampling distribution given [latex]\\mu[\/latex] and [latex]n[\/latex].<\/li>\r\n\t<li>Know and check the conditions of the Central Limit Theorem.<\/li>\r\n\t<li>Use the normal approximation to compute probabilities involving sample means when appropriate.<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Sampling Variability<\/h2>\r\n<p>Let's use simulations to explore the variability of the sample means.<\/p>\r\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Under <strong>Select Population Distribution<\/strong>, choose <strong>Bell-Shaped<\/strong>.<br \/>\r\n<strong style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Step 2: <\/strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Select the <strong>enter values for [latex]\\mu[\/latex] and [latex]\\sigma[\/latex]<\/strong>\u00a0option and enter each of the mean and standard deviation values accordingly.<br \/>\r\n<\/span><strong style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Step 3: <\/strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Use the slider or enter the value for the sample size [latex]n[\/latex].<br \/>\r\n<\/span><strong style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Step 4: <\/strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Select how many samples you want to simulate drawing from the population and click on <strong>Draw Sample(s<\/strong>).<br \/>\r\n<\/span><strong style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Step 5: <\/strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Click on <strong>Find Probability<\/strong>\u00a0to calculate the probability at or below a certain value.<\/span><\/section>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/sampdist_cont\/ \" width=\"100%\" height=\"1500\" 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\/sampdist_cont\/\" 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]964[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Create a sampling distribution given [latex]\\mu[\/latex] and [latex]n[\/latex].<\/li>\n<li>Know and check the conditions of the Central Limit Theorem.<\/li>\n<li>Use the normal approximation to compute probabilities involving sample means when appropriate.<\/li>\n<\/ul>\n<\/section>\n<h2>Sampling Variability<\/h2>\n<p>Let&#8217;s use simulations to explore the variability of the sample means.<\/p>\n<section class=\"textbox interact\"><strong>Step 1: <\/strong>Under <strong>Select Population Distribution<\/strong>, choose <strong>Bell-Shaped<\/strong>.<br \/>\n<strong style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Step 2: <\/strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Select the <strong>enter values for [latex]\\mu[\/latex] and [latex]\\sigma[\/latex]<\/strong>\u00a0option and enter each of the mean and standard deviation values accordingly.<br \/>\n<\/span><strong style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Step 3: <\/strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Use the slider or enter the value for the sample size [latex]n[\/latex].<br \/>\n<\/span><strong style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Step 4: <\/strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Select how many samples you want to simulate drawing from the population and click on <strong>Draw Sample(s<\/strong>).<br \/>\n<\/span><strong style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Step 5: <\/strong><span style=\"font-size: 1rem; orphans: 1; text-align: initial; background-color: initial; word-spacing: normal;\">Click on <strong>Find Probability<\/strong>\u00a0to calculate the probability at or below a certain value.<\/span><\/section>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/sampdist_cont\/\" width=\"100%\" height=\"1500\" 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\/sampdist_cont\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm964\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=964&theme=lumen&iframe_resize_id=ohm964&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":8,"menu_order":11,"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\/1274"}],"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\/1274\/revisions"}],"predecessor-version":[{"id":6784,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1274\/revisions\/6784"}],"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\/1274\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1274"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1274"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1274"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1274"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}