{"id":1280,"date":"2023-06-22T02:13:13","date_gmt":"2023-06-22T02:13:13","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sampling-distribution-of-a-sample-mean-apply-it-4\/"},"modified":"2024-01-17T22:04:47","modified_gmt":"2024-01-17T22:04:47","slug":"sampling-distribution-of-a-sample-mean-apply-it-4","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/sampling-distribution-of-a-sample-mean-apply-it-4\/","title":{"raw":"Sampling Distribution of a Sample Mean: Learn It 4","rendered":"Sampling Distribution of a Sample Mean: Learn It 4"},"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;Create a sampling distribution given [latex]\\\\mu[\/latex] and [latex]n[\/latex]&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;}\">Create a sampling distribution given [latex]\\mu[\/latex] and [latex]n[\/latex].<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Know and check the conditions of the Central Limit Theorem&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;}\">Know and check the conditions of the Central Limit Theorem.<\/span><\/li>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the normal approximation to compute probabilities involving sample means when appropriate&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;}\">Use the normal approximation to compute probabilities involving sample means when appropriate.<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>Ultimately, we would like to develop a probability model based on this sampling distribution. We use the probability model with an actual sample mean to either estimate or test a claim about a population mean.<\/p>\r\n<p>Let's calculate probabilities using the mean and standard deviation of the sampling distribution of the sample mean.<\/p>\r\n<p><iframe src=\"https:\/\/lumen-learning.shinyapps.io\/normaldist\/ \" width=\"100%\" height=\"600\" 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\/normaldist\/\" 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]900[\/ohm2_question]<\/section>\r\n<section>\r\n<section class=\"textbox watchIt\">[reveal-answer q=\"676221\"]See the example question[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"676221\"][ohm2_question hide_question_numbers=1]1181[\/ohm2_question][\/hidden-answer]<br \/>\r\n[videopicker divId=\"tnh-video-picker\" title=\"Sampling Distribution of a Sample Mean\" label=\"Select Instructor\"]<br \/>\r\n[videooption displayName=\"Dr. Aris Winger\" value=\"https:\/\/www.youtube.com\/watch?v=Eaqq6p_qb8Q\"][videooption displayName=\"Dr. Pamela E. Harris\" value=\"https:\/\/www.youtube.com\/watch?v=03XsGXiiOdE\"] [videooption displayName=\"Dr. Lane Fisher\" value=\"https:\/\/www.youtube.com\/watch?v=ukDT-ql8EKY\"]<br \/>\r\n[\/videopicker]<\/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;Create a sampling distribution given [latex]\\\\mu[\/latex] and [latex]n[\/latex]&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;}\">Create a sampling distribution given [latex]\\mu[\/latex] and [latex]n[\/latex].<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Know and check the conditions of the Central Limit Theorem&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;}\">Know and check the conditions of the Central Limit Theorem.<\/span><\/li>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Use the normal approximation to compute probabilities involving sample means when appropriate&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;}\">Use the normal approximation to compute probabilities involving sample means when appropriate.<\/span><\/li>\n<\/ul>\n<\/section>\n<p>Ultimately, we would like to develop a probability model based on this sampling distribution. We use the probability model with an actual sample mean to either estimate or test a claim about a population mean.<\/p>\n<p>Let&#8217;s calculate probabilities using the mean and standard deviation of the sampling distribution of the sample mean.<\/p>\n<p><iframe loading=\"lazy\" src=\"https:\/\/lumen-learning.shinyapps.io\/normaldist\/\" width=\"100%\" height=\"600\" 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\/normaldist\/\" target=\"_blank\" rel=\"noopener\">Trouble viewing? Click to open in a new tab.<\/a>]<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm900\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=900&theme=lumen&iframe_resize_id=ohm900&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section>\n<section class=\"textbox watchIt\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q676221\">See the example question<\/button><\/p>\n<div id=\"q676221\" class=\"hidden-answer\" style=\"display: none\"><iframe loading=\"lazy\" id=\"ohm1181\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=1181&theme=lumen&iframe_resize_id=ohm1181&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/div>\n<\/div>\n<div class=\"wp-nocaption \"><\/div>\n<div id=\"tnh-video-picker\" class=\"videoPicker\">\n<h3>Sampling Distribution of a Sample Mean<\/h3>\n<form><label>Select Instructor:<\/label><select name=\"video\"><option value=\"https:\/\/www.youtube.com\/embed\/Eaqq6p_qb8Q\">Dr. Aris Winger<\/option><option value=\"https:\/\/www.youtube.com\/embed\/03XsGXiiOdE\">Dr. Pamela E. Harris<\/option><option value=\"https:\/\/www.youtube.com\/embed\/ukDT-ql8EKY\">Dr. Lane Fisher<\/option><\/select><\/form>\n<div class=\"videoContainer\"><iframe src=\"https:\/\/www.youtube.com\/embed\/Eaqq6p_qb8Q\" allowfullscreen><\/iframe><\/div>\n<\/section>\n<\/section>\n","protected":false},"author":8,"menu_order":10,"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":[{"divId":"tnh-video-picker","title":"Sampling Distribution of a Sample Mean","label":"Select Instructor","video_collection":[{"displayName":"Dr. Aris Winger","value":"https:\/\/www.youtube.com\/embed\/Eaqq6p_qb8Q"},{"displayName":"Dr. Pamela E. Harris","value":"https:\/\/www.youtube.com\/embed\/03XsGXiiOdE"},{"displayName":"Dr. Lane Fisher","value":"https:\/\/www.youtube.com\/embed\/ukDT-ql8EKY"}]}],"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\/1280"}],"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\/1280\/revisions"}],"predecessor-version":[{"id":5118,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1280\/revisions\/5118"}],"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\/1280\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1280"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1280"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1280"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}